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 Commodity (Gold) Trading Report  
  The purpose of writing this report is to give reader depth knowledge of the derivative markets like Futures, Forwards and Options and their prices derivation and future price analysis. The choice of the Futures, Forwards and Option markets together was made because they are fundamentally well related to each other and they are now a day most important instrument for risk management. In this decade, these instruments have grown rapidly and understanding and knowledge of pricing of these instruments would be the advantage.

I will focus on understanding of price derivation for each market. I will undergo basic concepts of Future, Forward and Option markets as they are vital for understanding market function and their theories on determining and forecasting price.

At the starting of all market introduction there are understandings of concepts used in the market, than there are brief discussions on the pricing theories; basically, there are two pricing theories on Options market and there are three theories on Futures market. At the end of an essay, after giving very good idea of all theories and concept, you will find an analysis about which theory is appropriate to predict the price or which are very helpful for trader to reduce his risk for particular contract or for particular market. With the help of Reuters 3000 Xtra we will go throw with practical example for pricing the contract.
  Trading of basic commodities is one of the oldest commercial activities found in every civilization. For all basic and omissible needs of the humankind, nearly every civilization developed some sort of central marketplace where people could meet and trade. This is when physical or cash market born. Over time, more participants entered this physical market directly or indirectly, thus price (value) of the commodity was directly depend on prolong market chain (e.g. processed, transported, stored, refined, manufactured, etc.). Each participant in the chain added value to the commodity and this affected the price to move up or down according to the supply and demand of the commodities in the chain. A sudden change in the supply/demand equation can create move in the price. If anyone in the chain needing to acquire a commodity then it causes sudden jumps in value and if he required holding a commodity decrement in value occurs.

The modern civilization introduced another level of risk. Merchants began writing individual contracts for expected deliveries, “forward contracts”, containing specific terms of delivery (quantity, quality, anticipated date of delivery) all for a fixed price. By this merchandisers start taking risk of weather, production, quality and natural disasters. With this increasing cash market risk, merchants for several basic commodities joined together in the late nineteenth century to establish a more organized and specialized marketplace at the TransAtlantic route (e.g. London and New York) for each commodity where they could meet and negotiate these forward contracts. The forward contract, however, was still a cash market instrument whereby a price was negotiated for an actual physical commodity transaction at a future date of delivery. The contract applied to the unique terms of one transaction, but the existence of this piece of paper added another possible level of trade – the idea of buying and selling the contract itself.

As a binding instrument that committed the holders to a transfer of the physical commodity, the contract itself could change hands many times as long as its terms remained outstanding (until the actual delivery took place). As the buying and selling of an existing contract became an accepted practice, the standardization of that contract became the next logical step. The standardization of the forward contract led to the creation of the futures contract that added a whole new dimension to the trade. The cash market continued its day-to-day business of selling and buying an asset at that day’s price. The organization of merchants buying and selling the physical asset evolved into an organization that standardized the contracts and the trading practices, and became the futures exchange. The acceptance of the standard contract allowed organized trading of the value of the asset for delivery at some future date through a futures market for that asset. The futures contract had specific terms, amount, type, price, timeframe, etc., but unlike the forward contract, it did not apply to any specific transaction. A “standard” contract with standard terms that applied across the board was developed. The underlying asset could change hands under the terms of the contract, but that was not its purpose – its purpose was to establish a price for the underlying asset for a defined period of time (the term of the contract). This price became a benchmark for determining the day-to-day cash market price. It also established the futures contract as an instrument that had its own value.

For traders who do not want to take any risk in the market, a new tool of risk management was introduced. Such a contract which is similar to futures contract when prices are in favour but when the price of the underlying asset was not in the favour, traders were given option of not bearing loss more then they choose to. An Option contract was introduced to limit the loss in futures contract. As a writer of the option contract was bearing the risk of unfavourable price changes the premium was paid to writer of the contract, this led this contract to have its own value. In the prior period when contract was introduced it was traded OTC (Over the Counter), these contracts were not standardized and both party involved in the contract had to bear the credit risk.
 Forward Contracts  
  A Forward contract is a transaction made now to purchase an asset, a specified amount of cash asset at a specific price with the exchange of funds or other contract as an underline asset at an agreed-upon time in the future. Each forward contract can be made on different terms. For¬ward transactions are completed every day for agricultural commodities, Treasury se¬curities, foreign currencies, and interest rate agreements made all over the world. For example, a farmer often makes a forward contract with an intermediary (called a "grain eleva¬tor") whereby the farmer agrees to sell grain to the elevator after harvesting. This con¬tract specifies the number of bushels of grain, the price per bushel, and the delivery date of the grain. This forward contract allows the farmer to plan for the future with the certainty of a profit, barring a natural weather disaster.  
 Futures Contracts  
  Futures contracts standardize the agreement between a buyer and a seller, specifying a trade in an underlying cash asset for a given quantity at a specific time. Two impor¬tant advantages of a futures contract are its tradability and its liquidity (i.e., one can trade large positions without affecting prices). In addition, one can profit with a futures contract without having to buy the cash asset. Futures exist because they provide risk and return characteristics that are not available solely by trading cash instruments such as stocks and bonds. Speculators can obtain very high rates of return with futures due.  
 Options Contracts  
  An option is a contractual agreement that gives the holder the right to buy or sell a fixed quantity of a security or commodity (for example, a commodity or commodity futures contract), at a fixed price, within a specified period of time. May either be standardized, exchange-traded and government regulated or over-the-counter, customized and non-regulated.  
 Differences between Forward, Futures and options  






Future agreement that obliges the buyer and seller

Future agreement that obliges the buyer and seller

Future agreement where the seller is obliged, but the buyer has an "option" but not an obligation

Contract Size

Depending on the transaction and the requirements of the contracting parties.



Expiry Date

Depending on the transaction


Standardised. American style options can be exercised at any time. European style options can only be exercised at expiry.

Transaction method

Negotiated directly by the buyer and seller

Quoted and traded on the Exchange

Quoted and traded on the Exchange


None. It is very difficult to undo the operation; profits and losses are cash settled at expiry.

Both parties must deposit an initial guarantee (margin). The value of the operation is marked to market rates with daily settlement of profits and losses.

The buyer pays a premium to the seller. The seller deposits an initial guarantee (margin) with subsequent deposits made depending on the market. The underlying asset can be used as guarantee.

Secondary Market

None. It is difficult to quit the operation; profit or loss at expiry.

Futures Exchange. Operation can be quit prior to expiry. Profit or loss can be realised at any time.

Options Exchange. Operation can be quit prior to expiry. Profit or loss can be realised at any time.

Institutional Guarantee

The contracting parties

Clearing House

Clearing House



Cash settled.

Contracts are usually closed prior to expiry by taking a compensating position. At expiry contracts can be cash settled or settled by delivery of the underlying.

When a long position is exercised it may be settled by delivery or cash settled. A long position which is out-of-the-money is usually cancelled prior to expiry.

 Futures/Forwards Market  
  Hedging is a risk reduction strategy whereby investors and traders take offsetting positions in an instrument to reduce their risk profile. Hedging is the process of managing the risk of metal change by offsetting that risk in the futures market.

Hedger is an individual or a firm who undertakes in hedging process. Usually a big firm who has big stock in hand or a big gold mine that has to protect itself for price risk.

A buy position or "long" in the underlying asset is covered by a sell position or "short" position in futures. Conversely, a "short" position in the underlying asset is covered by a buy position or "long" in futures. The greater the correlation between the changes in prices of the underlying asset and the futures contract the more effective the hedge. As such, the loss in one market is partially or totally compensated by the profit in the other market, given that the traded positions are equal and opposite.
  Speculation involves the buying, holding, and selling of stocks, commodities, futures, currencies, collectibles, real estate, or any valuable thing to profit from fluctuations in its price as opposed to buying it for use or for income ( via dividends, rent etc). Speculation represents one of three market roles in western financial markets, distinct from hedging and arbitrage.  
  Type of Speculation  
  Passive Speculation: When a spot position is held or expected to be held without any type of hedge, it can also be classed as passive speculative.

Active or Dynamic speculation: A speculative operation aims to profit from expected differences in quotations, based on taking positions on the basis of with expected trends.
  The speculator tries to maximise profits in the shortest period of time, thus reducing the investment of personal funds.

The high degree of financial leverage that is obtained with futures contracts makes them particularly appealing to speculators, as the multiplier effect on profits in active speculative trades are seen as especially attractive when the trend in quotations is correctly predicted.

Most non-professional traders lose money on speculation, while those that do make money tend to become professional.
  The Economic Role of Speculation  
  The roles of speculators in a market economy are to absorb risk and to add liquidity to the marketplace by risking their own capital for the chance of monetary reward. A speculator will exploit the difference in the spread and, in competition with other speculators, reduce the spread thus creating a more efficient market. It is positive for the overall operation of the market as it brings greater liquidity and stability, as well as greater range, flexibility and depth in contract quotations.  
  An arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets: combinations of matching deals are struck that exploit the imbalance, the profit being the difference between the market prices. A person who engages in arbitrage is called an arbitrageur.

An arbitrage is an opportunistic operation that usual exists for very short time periods. Arbitrage trading includes a wide range of crossed operations, of which the most frequent and representative are arbitrages on futures-spot, futures-options, futures-options with different expiries and matching or similar futures and options quoted in different exchanges.
  The Economic Role of Arbitrage  
  In Economics, The activity of the arbitrageur ensures that prices tend to efficiency. Thus, we should consider the role of the arbitrageur as both positive and necessary for the overall operation of the market.  
 Pricing Futures Market  
 Capital Asset Pricing Model  
  The Capital Asset Pricing Model (CAPM) has been widely applied to all kinds of financial instruments. It states that the return on a security is a function of the market (systematic) risk.  
  Assumptions of CAPM  
  [1.] Capital markets are perfect, there is only a single borrowing and lend¬ing rate no transaction costs, all capital assets are perfectly divisible (one can buy fractions of a security) and there are no taxes, investors can sell short and information is freely available to all market participants.
[2.] Investors attempt to maximize their utility, which consists of maximiz¬ing returns for a given level of risk. Investors are risk-averse and measure risk in terms of standard deviations of returns.
[3.] Investors use a common one-period-ahead time horizon for investment decisions. All investment decisions are made at the beginning of the period and no changes are made during the investment horizon.
[4.] Investors have identical expectations about the risk and return.
[5.] There exists a single risk-free asset at which borrowing and leading can take place.
  The Model  

E(Rj) = Rf +ßj[E(Rm) - Rf]

E(Rj) = the expected return on security j
Rf = the risk-free rate
E(Rm) = the expected return on the market portfolio
ßj = cov(Rj, Rm)/σ2 = The Beta of the instrument

  The Capital Asset Pricing Model is denned by in above equation, where the measure of systematic risk (ß) is the covariance of the asset return (futures price change) with the return on the market portfolio (index), divided by the variance of the market return (index return);

It is an important theory for pricing stocks and portfolios of stocks. For futures pricing it states that futures price is directly related in a proportional to the “market”, the proportional is systematic risk and it is measured by ß. The beta is usually estimated from a regression equation where ß measure the systematic risk and standard deviation of the error tells us about the unsystematic of the market:

Rj = α + ßjRm + ej

ßj = the systematic risk of security j
σ(ej) = the unsystematic risk of security j

  According to the CAPM, only unavoidable risk should be compensated in the marketplace, and traders can avoid much risk through diversification. Even after diversification, risk remains because the returns are correlated with the market as a whole. This remaining risk is systematic. So if ß = 1 then asset has the same degree of systematic risk as the market portfolio. So the asset should earn same return as the market portfolio. If ß = 0 then asset should only earn risk free rate of interest.

In contexts to futures market if we put this logic then if the ß is more then zero then expected futures price is positive which means expectation of futures pries should be more then spot price. If the ß is zero then there shouldn’t be any change in future price as there is no investment on it. However, there is a margin to pay but it is not so called investment as it is in a form of the deposit against the price fluctuation and price risk.
 The Hedging Pressure Theory  
  Assume for the moment that speculators are rational and risk adverse. The hedging pressure theory of future pricing comes from the view point of speculators. If the futures price reaches the expected price of the commodity when the futures contract matures, then there is no reason for speculators to speculate in futures. Speculators will only come to contract if they have been compensated for the risk they have been taking. When net long hedger exist net short speculators, this require speculators to take more short position or when net short hedger exist net short speculators this require speculators to take more long position, for to bear this an extra risk the speculator will want above-average returns to enter in contract. These above-average returns will be compensated by moving futures price to the favour to speculator. This theory work simply works like demand and supply theory demand goes up price go up.

The hedging pressure theory of future pricing is if net short hedging exceeds net long speculation, then long speculators require above-average returns compensation for purchasing additional futures contracts in order to equate supply and demand the relationship is known as normal backwardation; that is, futures prices must be underpriced relative to their true value to encourage speculators to buy futures. Similarly contango means that futures must be overpriced for short speculators to earn abnormal return when net long hedging is greater then net short speculation, by this supply-and demand factor could cause the futures to be consistent under –or overpriced relative to its true value.

Although the number of long positions must equal the number of short positions for trading to exist, the hedging pressure theory states that when a net short or long hedging position exist, the futures contract becomes a biased estimate of the spot price. These biased prices encourage additional speculators to enter the market and create the needed activity to offset the hedger’s activity in the market. Now let’s take the real example of the backwardation theory in real market. .(Robert T. Daigler,1994)
  Heating Oil Futures Pricing:  
  Heating Oil futures price is the best example the theory of the normal backwardation Even though the costs of storage and transport are high, the heating oil future pricing is regional, inventory is low relative to consumption; demand is seasonal; and the risks of a supply interruption (OPEC supply cutbacks, a refinery explosion) are real, many key market participants can’t afford the risk of selling inventory and going long on heating oil futures if a spot-futures pricing arbitrage opportunity presents itself. Certain participants have to hold inventory. For holding the inventory the participant is giving convenience yield to the speculator. And because of the convenience yield it is very hard execute the arbitrage and maintain price efficiency. It is all these factors, but especially the last one, that weaken the force of arbitrage to maintain price efficiency with consumption commodities. The result is the following inequality for pricing consumption commodity futures contracts:  


  The convenience yield is the amount paid to the speculators by the hedgers to enter in the contract. It is the difference between arbitrage-free efficient futures price and the spot price. The convenience yield reflects the market’s expectations concerning the future availability of the commodity. The greater the possibility that shortages will occur during the life of the futures contract, the higher the convenience yield. If we take out the convenience yield (y) from the spot price then we can get the arbitrage free, efficient futures price.  

F0-T = S0e(r+w-y)T

  Summery of Studies of Normal Backwardation:  


Key Results


Found positive returns for cotton, wheat, and corn.

Rockwell (1967)

Found little support for normal backwardation.


Found returns near zero for wheat, corn, and soybeans.

Bodie and Rosansky (1980)

Found positive returns for many commodities.

Carter, Rausser, and Schmitz (1983)

Found positive returns in wheat, corn, and soybeans.

Raynauld and Tessier (1984)

Results for corn, wheat, and oats did not support normal backwardation.

Chang (1985)

Examined wheat, corn, and soybeans, but results were inconclusive for normal backwardation.

Baxter, Conine, and Tamarkin (1985)

Found no positive returns for wheat, corn, or soybeans.

Park (1985)

No normal backwardation in currencies and plywood, but normal backwardation in metals.

Hazuka (1984)

Evidence from applying the consumption-based CAPM to 14 commodities, supported normal backwardation.

Fama and French (1987)

Found positive returns that weakly support normal backwardation.

Ehrhardt, Jordan, and Walkling (1987)

Found no support for normal backwardation in wheat, corn, or soybeans.

Hartzmark (1987)

Found that hedgers made money and speculators lost money, which is inconsistent with normal back­wardation.

Yoo and Maddala (1991)

Large hedgers pay some risk premium, and profits of large speculators are due mostly to risk bearing.


Of 29 commodities tested, only four conform well to the backwardation hypothesis. Backwardation is not a general feature of futures markets.

Deaves and Krinsky (1995)

Provided a more detailed examination of the commodi­ties that Kolb (1992) found to be candidates for back­wardation. Found that futures prices are good predictors of subsequent spot prices.

 Cost-of-carry Model  
  The Model  
  The Cost-of-carry is the total cost to carry a good forward in time. For example gold on hand in June can be carried forward up to, stored until, December. So the price of December contract will be June contract plus cost of carrying gold to December. It is an arbitrage-free pricing model. Its central theme is that futures contract is so priced as to prevent arbitrage profit. In other word, investors are not paying less or more in either spot or future market for executing their buying and selling contract or underline asset. It is because future prices are effectively priced by considering the interest gain or loss via holding or selling contract and other expenses paid for holding the underline assets. It is true that expectations do influence the price, but they influence the spot price and, through it, the futures price. They do not directly influence the futures price. According to the cost-of-carry model, the futures price is given by  
  Futures price = Spot Price + Carry Cost - Carry Return  

F = S + C – R

F = Future price
S = Spot Price
C = Carry Cost
R = Carry Return
  Carry cost has basic four categories: storage costs, insurance costs, transportation costs and financing cost. Storage cost involves the cost of warehousing of the commodity in the appropriate facility. Storage cost plays key role in physical goods and a goods which could be stored for long period of the time like gold, silver, wheat, lumber etc. For most of the goods in storage insurance is also necessary. For example insurance on lumber for fire, on gold or silver for theft, on wheat for water damages.

Financing cost is the cost of risk free interest that investors have to pay or have to receive according to their position. Most of the time in futures market instead of the taking physical deliveries of an underline asset investor go for the cash settlement, investor simply take the opposite position and get out of the contract. Because of it insurance, transportation and storage cost are irrelevant but even if it is cash settlement investor has to pay financing cost directly or indirectly. That’s why financing cost is most important cost for the cost-of-carry model.

Carry return is the income (e.g., dividend, interest gain) derived from underlying asset during holding period. Thus, the futures price should be equal to spot price plus carry cost minus carry return. If it is otherwise, there will be arbitrage opportunities as follows.
  Examine the Model  
  To prove that futures price has to be equal spot price plus carry cost minus carry return lets see what happen when it is not so:

Lets take when F > (S+C –R) then we can sell the overpriced futures contract and buy the underline asset in the spot market and hold until the maturity. On maturity we give the delivery of the underline asset and we earn the difference. This is called "cash-and-carry" arbitrage.

Now as per assumption of perfect market everybody knows this and everybody tries to take advantage of the "cash-and-carry" arbitrage. Now at time 0 everybody tries to sell the futures contract in futures market and tries to buy the underline commodity on spot market because of this the supply for the futures contract in futures market will be increased and demand for the underline asset will increase in spot market. Now as per demand and supply law the access supply will lead to drop the price of future contract in futures market and access demand will lead to increase in the price in the spot market. The increment in price of spot market and decline in the futures market will continue until the futures price should be equal to spot price plus carry cost minus carry return. So we can say that this can’t hold in long run.

Lets take when F > (S+C –R) then we can buy the underpriced futures contract and short-sell the underlying asset in spot market and invest the proceeds of short-sale until the maturity of futures contract. On maturity we take the delivery of the underline asset and sell the futures contract. This is called "reverse cash-and-carry" arbitrage.

Now as per assumption of perfect market everybody knows this arbitrage and everybody tries to take advantage of the "reverse cash-and-carry" arbitrage. Now at time 0 everybody tries to buy the futures contract in futures market and tries to short-sell the underline asset on spot market because of this the demand for the futures contract in futures market will be increased and the supply of the money in money market will increase. Again, as per demand and supply law the access demand will lead the increment of price of future contract in futures market and access supply will lead the decline in the interest rate in money market. The increment in price in futures market and decline in interest rate will continue until the futures price should be equal to spot price plus carry cost minus carry return. So we can say that this can’t hold in long run.

Thus, in long run futures price will be same as spot price plus carry cost minus carry return which means it makes no difference whether we buy or sell the underlying asset in spot or futures market. If we buy it in spot market, we require cash but also receive cash distributions (e.g., dividend) from the asset. If we buy it in futures market, the delivery is postponed to a later day and we can deposit the cash in an interest-bearing account but will also forego the cash distributions from the asset. However, the difference in spot and futures price is just equal to the interest cost and the cash distributions.
  Cost of Carry with Different Markets  
  Basic Cost-Of-Carry  
  Cost-of-carry model can also determine the price relationships that can exist between futures contracts on the same good that differ in maturity. According to Cost-of-carry model future price of distance contract must be equal to future price of nearby contract plus carry cost.  

Fd = Fn + C - R

Fd = Distance Future contract
Fn = nearby Future Contract
C = Carry cost
  As we have proved above, we can also prove that Futures price of distance contract can’t be either less than or more than the future price of the nearby contract plus carrying cost.

The pricing of futures contract in every market is also different form each other because the fundament for underline asset in each market is different. These Fundaments create the equation of the carry cost. Most of the time carry cost is the interest we pay or give in every market.
  Storable Non Income Generating Commodities  
  There are a number of interest rates in the economy, even for the same period. There are deposit rate, lending rate, repo rate, Treasury bill yield, etc. Since the Clearing Corporation guarantees the futures contract, it is a risk-free asset, like treasury bills. Accordingly, the interest rate factored in futures price should be the interest rate on risk-free assets like treasury bills. This is called the "risk-free rate." There is no subjectivity or uncertainty about carry return. Most commodities fall into this category and the fair value (or theoretical value) of the futures contract is determined by the following equation:  
  F = S(1 + r)t/365  
F = Fair value of a Futures contract expiring in t days using Compounding Interest Rate
P = Current spot price of underlying assets
r = Carry cost (largely interest charges)
t = Days to settlement
  Stock Market Futures  
  In stock market as well interest rate has the largest proportion of carry cost. The equation for futures price gives the current price whereas the cash dividend is payable sometime during contract life. To bring all terms on a common footing, we will have to use the present-value of cash dividend rather than the dividend amount itself. Let us now examine the carry cost, which is essentially the interest rate. We can now translate the futures pricing equation in computable terms as follows.  

F = S + (S r T) - (D - D r t)

F = futures price
S = spot price
r = risk-free interest rate (pa)
D = cash dividend from underlying stock
t = period (in years) after which cash dividend will be paid
T = maturity of futures contract (in years)
  It is customary to apply the compounding principle in financial calculations. With compounding, the above equation will change to  

F = S(1+r)T - D(1+r)-t

  Alternately, using the continuous compounding or discounting,  

F = SerT - De-rt 

  There are two good reasons why continuous compounding is preferable to discrete compounding in stock market. First, it is computationally easier in a spreadsheet. Second, it is internally consistent. For example, interest rate is always quoted on an annual basis but the compounding frequency may be different in different markets.  
  Equity Stock Index  
  In Equity Stock Index, we consider the portfolio of shares held in the index. Then we discount it by short-term rate and the dividend yield of the market.  

 F = P(1 x r/100 - d/100) t/365

P = All-Share Index times the contract size
r = short-term rate
d = dividend yield
t = number of days between futures trading date and expiry date
  Stock index futures closely follow the price movement of their respective indexes, typically referred to as the “underlying” or “cash” indexes. Intraday, monthly, and yearly correlations between cash indexes and futures are very close. On some occasions, the futures may diverge from the cash index for short periods of time, but market forces (such as arbitrage) usually work to bring these brief variances back into line.  
  Currency Futures  
  The fair value of a currency futures contract is largely determined by the interest rate differential between deposits in different currencies (interest rate parity).
The following formula is used to establish the fair value of a currency futures contract (which is also the forward exchange rate):

Fx = [1 + (rf x t/365)]/[1 + (rd x t/365)] x Fs

Fx = forward exchange rate expressed in foreign currency units
Fs= current spot exchange rate expressed in foreign currency units
rf = current foreign interest rate
rd = current domestic interest rate
t = number of days between futures trading date and futures
  Currency trade nowadays done on forward exchange rather then futures exchange so futures price tend to be same as forward price.  
  Calculating the Currency Futures price in Real world  
  Now By using Cost and carry model for currency futures, let us calculate the future price of the Swiss franc in the real world it always tends to be the interest rate differential between deposits in different currencies (interest rate parity).
For example, assume we are in March, so to get Swiss Franc 3 month forward rate means June’s forward rate. Now by using the Reuters Xtra 3000 pro, we can get the spot rate of the Swiss franc (CHFF=) the Spot price for sell Swiss franc is 1.6771 and for the bid price of the 3 months interest in Switzerland check (CHF3M=) which -0.00129 rounded 0.0013.
Forward rates’ upper range is calculated as
1.6771 - 0.0013 = 1.6758
For lower range buy price in spot market (CHFF=) is 1.6781 and ask price of the 3 months interest is 0.0009.
Forward rates’ lower range is calculated as
1.6781 - 0.0009 = 1.6772.
  As Swiss franc forward price are quoted in the Swiss franc we have inversed our result. The result we will get is 0.5967 and 0.5962. Which means forward rate must be in range of 0.5967 to 0.5962. If we see the June Forward’s last price (JUN2: 0#SF) then find that It is 0.5964 which is in the rage.  

  An option is a contract between two parties, where buyer of an option contract acquires right but not an obligation of buying or selling the underline an asset on a determined quantity of at certain price at any point of time in future from writers of an option contract.  
  There are two type of Option contract traded in markets:
• Option contract to buy (call).
• Option contract to sell (put).
  Likewise in futures there are two basic strategies, namely to buy and to sell contracts, in options there are four basic strategies as follows:  
  • Buy option contract to buy (long call).
• Sell option contract to buy (short call / Write call).
• Buy option contract to sell (long put).
• Sell option contract to sell (short put / Write Put).
  As in futures contract the buyer of a contract has a right as well as the obligation of buying or selling the contract at expiry date. Whereas, this obligation is broken in options where the buyers of the contract has the right but not obligation to buy (call) or sell (put), where writer (seller) of the option only has the obligation to sell (call) or to buy (put) the underline asset. As the seller of the writer the price risk, he requires a premium which has been paid by the buyer of the contract up front. There always been a credit risk while dealing with any contract related to any future transaction. To make an option popular there has to be done something to eliminate the credit risk. Here the solution came from the old concept “the exchange place”, which is a common place where all the buyers and seller come for trading and exchange barriers the credit risk for the both parties.

An option has been made up with five fundamental characteristics like:1) type of option (buy -call or sell - put), 2) the underlying asset or reference, 3) the amount of the underlying that the option gives right to buy or sell, 4) the expiry date and 5)the exercise price of the option.

An Option which can be exercised at any moment up to expiry is called an American options or and which can be only exercised at expiry is a European options.
 Jargons of Option Market  
  In every market there are my words used as some specific term or concept. In option market there are most popular jargons are in the money, at the money, or out of the money. At any define time t; an option may be in the money, at the money, or out of the money.

At the money: When the Strike Price of call is same as the current stock price then that call is said to be at the money. Call in most liquid at this position.

In the money:- When the strike price of call is more then current stock price, which means the call can be excised on write. That call is said to be in the money call. If the difference between strike price and stock price is too large then that call is said to be deep-in-the-money.

Out of the money:- When the strike price of call is less then strike price current stock price, which means the call can not be excised on write in near future. That call is said to be out of the money call. If the difference between stock price and strike price is huge, then that call is said to be deep-out-of -the-money.

For put, these terms are reversed means out of the money call is in the money for put and so on so for.
 Call Premium Value  
  We can brake an option's premium into two parts: intrinsic value (some¬times called parity value), and time value (sometimes called premium over parity).  
  Table: Out, In and At the money  





In the money

Out of the money



  Intrinsic Value: Difference between strike price and the stock price is called intrinsic value, if the value of the difference is more then zero then and then intrinsic value is taken into the account and that’s why intrinsic value comes into account in premium calculation when option is In-the-money. The intrinsic value of the premium will be zero if the call is at the money or out of the money.  

S – K   if S > K

Intrinsic Value =

0                if S ≤ K

Which means the intrinsic value of a call is the greater of 0 or St — K.

  Time Value: Time value is the difference between the option premium and the intrinsic value. The structure of the time value can also be broken in two parts first is present value of the amount of stock price and second is the compensation amount that buyer of the call pays to the writer of the call for taking the price risk. Usually, the maximum time value exists when the call (or put, for that matter) is at the money because writer of the call is having more price risk then to Out of the money or In the money call. As buyer of the in the money call takes price risk so there is no time value in the In-the-money call C = S – K and other way round in out of the money call writer is barring the price risk the time value is higher then the intrinsic value that’s why C > S – K, the longer the time period the greater time value all else equal.  
  Time value of a call = C, - {max[0, St - K]}  
  Similar is with put:  

K - S    if K > S

Intrinsic Value =

0           if K ≤ S

  It means puts intrinsic Value will be Max (0, K – S) and about time value of the put all put which is In the money or Out of the money has it but put at the money may or may not have the time value. (David A Dubofsky, 1992)  
 Pricing Options  
  Pricing options is a foundation of the finance. There are popular two methods used for the pricing Options. First in 1970s The Black Schole model coincided with initiation of exchange-traded options on the Chicago board of exchange in 1973. Then the innovation of Black Schole model came which called Binomial Model is now more popular and more used.  
 The Binomial Option Pricing Model (BOPM)  
  The binomial option pricing model has proved over time to be the most flexible, intuitive and popular approach to option pricing. It is based on the simplification that over a single period (of possibly very short duration), the underlying asset can only move from its current price to two possible levels. Among other virtues, the model embodies the assumptions of no riskless arbitrage opportunities and perfect markets. Neither does it rely on investor risk aversion or rationality, nor does its use require estimation of the underlying asset expected return. It also embodies the risk-neutral valuation principle which can be used to shortcut the valuation of European options. In addition, we show later, that the Black-Scholes formula is a special case applying to European options resulting from specifying an infinite number of binomial periods during the time-to-expiration.  
  Perfect Market Assumptions
• Equilibrium
• Perfectly competitive
• Existence of risk free asset
• Equal access to the capital market
• Infinitely divisible securities
• Perfect Short-selling allowed
• No transaction costs or taxes

Other Assumptions:
• Only one Interest rate for landing and borrowing
• Periodic interest rate and size of up tick and down tick know in every future period.
• Stock moves according to “Geometric Random Walk”
• Investor prefers more wealth to less.
  One Period Pricing Model  
  The basic assumption in the any Binomial pricing model is the stock price follows a multiplicative binomial process over discrete periods. The rate of return on the stock over each period can have two possible values: 1+ u with probability p, or 1+d with probability 1 – p. Thus, if the current stock price is ST-1, the stock price at the end of the period will be either (1+u)S or (1+d)S. This movement can be represented with the following diagram:  

                                                 (1+u)St T-1 =ST,u           with probability p


                                                (1+u)ST-1 =ST,d             with probability 1 - p

  If “ r” represent one plus the riskfree interest rate on the stock price S, over one period of time then to make no arbitrage it has to hold u > r > d, if these inequalities did not hold, there would be profitable riskless arbitrage opportunities involving only the stock and riskless borrowing and lending.

To find out the price of the call on this stock whose expiration date is just one period away lets take CT-1 be the current value of the call, C(1+u) = CT,u = max ( 0, ST,u – K) be its value at the end of the period if the stock price goes to ST,u and C(1+d) = CT,d = max ( 0, ST,d – K) be its value at the end of the period if the stock price goes to ST,d. where max ( 0, ST,d – K) comes from the concept of call premium calculation on page 28. Therefore,

                                     C(1+u) = CT,u = max ( 0,  ST,u – K) with probability p


                                    C(1+d) = CT,d = max ( 0,  ST,d – K) with probability 1 – p

  Now suppose a portfolio containing  shares of stock and B dollar amount in riskless bonds is formed. So the portfolio will cost ST-1 + B. At the end of the period, the value of this portfolio will be:  

                                                 D(1+u)ST-1 + (1+r)B = DST,u + (1+r)B

                          DST-1 + B

                                                D(1+d)ST-1 + (1+r)B = DST,d + (1+r)B

  Where r is the riskfree interest rate u is the uptick and d is downtick. The value of the  and B in shows the risk adversity of the investors. As assumed that the investors are very risk adverse and wish not take any risk, so the end-of-period values of the portfolio and the call for each possible outcome must be same to attract the investor. So Value of  and ß will be:  

D(1+u)ST-1 + (1+r)B = CT,u

D(1+d)ST-1 + (1+r)B = CT,d

  Solving these equations,  


  The value of  refers to how many shares of stock to buy in order to replicate a call, where 0≤  ≤ 1.The value of B, where B≤ 0, specifies how much to borrow to finance the investment in the stock. If the call and the debt-equity portfolio both offer exactly the same payoffs at time T, then the price of the call at time T - 1 must equal the investment in the equivalent portfolio at time T – 1.If there are to be no riskless arbitrage opportunities, the current value of the call, C, cannot be less than the current value of the hedging portfolio, S + B. If it were, we could make a riskless profit with no net investment by buying the call and selling the portfolio. But this overlooks the fact that the person who bought the call, has the right to exercise it immediately.

Suppose that St-1 + B < S – K. If a person try to make an arbitrage profit by selling calls for more than St-1 + B, but less than S – K, then he will soon find that he is the source of arbitrage profits rather than the recipient. Anyone could make an arbitrage profit by buying our calls and exercising them immediately.

The conclusion is that if there are to be no riskless arbitrage opportunities, it must be true that
If St-1 + B is greater than S – K then,


Equation (2) can be simplified by defining


So new equation is:

C = [pCu + (1 – p)Cd]/(1+r )                (3)

, and if not, C = S – K.

  The Two-Period Pricing Model  
  The next possible situation in binomial model can be interpreted by two period pricing mode: pricing a call with two periods remaining before its expiration date. In keeping with the binomial process, the stock can take on three possible values after two periods.  


                                                            (1+u)2S T-2 = ST,uu

                                                (1+u)S T-2 =S T-2

         ST-2                                              (1+d)(1+u)S T-2 = ST,ud

                                                (1+d)S T-2 =S T-1

                                                                                    (1+d)2S T-2 = = ST,dd


  In above diagram (a) S T-2 is current stock price at the end of one period, T-1, the stock price can take two places, depending if it is an up tick or downtick. At the end of second period, T, the stock price can take three prices. Tick up-up which will be St,uu, tick down-down will be St,dd and note here tick can go up-down or down-up which will give the same answer but can be written different in ways which are St,du or St,ud. Here you will find it as a S.  
  Pricing Process for a call  

                                                                     CT,uu = max[0, (1+u)2S T-2 – K]                                                          

                                                   CT- 1,u

          CT-2                             CT,ud = max[0, (1+d)(1+u)S T-2 – K]

                                                   CT- 1,d

                                                                     CT,dd = max[0, (1+d)2S T-2 – K]

  In Diagram (b) CT,uu stands, for the value of a call two periods from the current time if the stock price moves upward each period; CT,dd for the stock price moves downward in both periods and CT,ud for one period going up and another period going down from current time here as well CT,du and CT,ud are giving same answers.

Now to find out the value of a call at current time CT-2 we start our calculation from left to right. So to get the values of CT,uu, CT,ud and CT,dd we will just get the difference between ST-2 and the strike price. Now the price of the CT-1,u and CT-1,d can be determined by using the one period model. In other word pretend current time is T-1 time and stock goes uptick or downtick. As said before the answer for both CTdu and CTud is same so modified formula (3) for this situation will be:


CT-1,u = [pCT,uu + (1 – p)CT,ud]/(1+r)

And                                                                                                                  (4)

CT-1,d = [pCT,du + (1 – p)CT,dd]/(1+r)


  Again, a portfolio with ST-2 in stock and B in bonds whose end-of-period value will be CT,uu if the stock price goes to ST,uu and CT,dd if the stock price goes to ST,dd. The functional form of  and B remains unchanged so to get the new values of  and B, simply use same steps as on to get equation (1) and change the CT,u and CT,d with the new values of CT-1,u and CT-1,d respectfully.

So now portfolios offer the exact same payoffs at time T-1. It means they are selling at same price at T-1. If they are selling at same price T-1 then they must sell for the same price at time T-2. So now we have

C T-2 = DST-2  + B

  If value of  and B is replaced in above equation:  

CT-2 = [p2Cuu + 2p(1 – p)Cud + (1 – p)2Cdd]/(1+r)2                          (5)



  A little algebra shows that this is always greater than S – K if, as assumed, r is always greater than one, so this expression gives the exact value of the call.  
  Multi Period BOPM  
  If the about formula (3) and formula (5) are observed then it can be seen that there is only one thing change in the formula(3) which led to formula (5) and that is number of period n. Now if the formula is statistically changed for any n period of time, by starting at the expiration date and working backwards, the general valuation formula can be determined for any n:  


  Where j is how many ways can an underline asset’s price reach a terminal value in a binomial process. In other word we say in n periods, how many ways can the stock realize j as an uptick.  
  Now if let a = minimum number of upticks needed to result in the call finishing in the money then if j ≤ a then call is worthless and value of the call became  


  This gives us the complete formula, but with a little additional effort we can express it in a more convenient way.  
 Black-Scholes’ Option Pricing Model  
  Now let take new step to words continuous-time version of binomial model by making the time periods smaller and smaller which tend n to be larger this is the basic insight of the Black-Scholes’ model. In this continuous-time version  
  • The individual interest payments become continuous compounding;
• The random walk becomes geometric Brownian motion;
• The binomial distribution of the number of price rises becomes a normal distribution.
  In binomial pricing model price movement was specified by the side of the price factors u and d. In the continuous-time black scholes’ model price movement is specified as drift parameter µ and the volatility parameter price σ. Under the standard assumption of no arbitrage  

µ = r −σ


  (Thomas, 2003,STX 2020)  
  [1.] Perfect Market
a. Capital Market is perfect. There is no transaction cost and taxes. There is no restriction on short selling. All assets are infinitely divisible.
b. All investors car borrow and land money at same riskless interest rate, which is constant over the life of the option.
c. Market is always open, full liquidity on buying and selling the contract and it is continuous.
[2.] Volatility
The volatility of the stock is accurately known and it is constant for the life time of the option contract.
[3.] Continuous time
One of Black and Scholes's main ideas was to work within a continuous timeframe. As a result, they obtained differential equations, which are easier to work with than discrete equations.
[4.] Brownian motion
The second key assumption was that relative price movements should be represented by Brownian motion. In fact, this was a default option because Brownian motion is the most "natural" process within a continuous time framework.
[5.] Arbitrage-free condition
The arbitrage-free condition (or absence or arbitrage) states that it is not possible to gain for sure without an initial outlay. Although this precept may seem trite, it is in fact the cornerstone of the whole argument.
  The Model  

C= SN(d1) – Ke-rTN(d2)

  Where S = The price of the underlying asset
K = The strike price of the call Option
r = risk free interest rate
T = time to expiration
N(d) = the cumulative standard normal distribution function
 = the standard deviation of the underlying asset’s return
In(S/K) = the natural logarithm of S/K
e-rT = the exponential function of –rT. e-rT is the present value of the factor when r is continuously compounded for T period of time Ke-rT is the present value of K.


  The model assumes that there value of σ and r remains constant. T is the number of months to expire.  
  Interpretation of N(d1) and N(d2)  
  The N(d1) and N(d2) terms are the cumulative probability functions which take into account the risk of the option being exercised. N(d1) is the cumulative probability relating to the current value of the underline assets it indicates by increasing one unit to the price how much the risk premium increases. The value of N(d1) lies between 0 and 1. If option is deeply out-of-the-money, then any unit rise in the price of underline asset will have little effect on the value of the call since it remains unlikely that the option will be exercised. If the option is currently at-the-money, then values of N(d1) will be 0.5 as there is a 50 per cent chance it will end up in-the-money and a 50 per cent chance it will end up out-of-the-money which means underline asset’s price increase by one unit price increase by 0.5 units. If the option is already deep-in-the-money, then unit rise in the price will have same unit rise in option price, and the values N(d1) will get closer to 1. The higher the stock price in relation to the price, the higher the value of N(d1). The value of the N(d1) is closely to value of delta of the stock.

N(d2) says the cumulative probability relating to the exercise price, it is the probability of call option will be actually exercised if N(d2) is 0.70 then there is a 70 percent chance that the option will be exercised. Normally the value of N(d1) is greater then N(d2) but when it is certain that option will be exercised then the values of both N(d1) and N(d2) is 1.
  The Volatility  
  The most controversial thing in the model is to measure volatility. Ideally, to get the an efficient pricing of option from this model one has to measure volatility that is likely to reflect the volatility that will occur in the future. There are three major way of calculating volatility:  
  • Implied volatility
• Expected volatility
• Historical volatility
  Expected Volatility: The Problem with Expected volatility is; it differs from one market participant to another, and therefore the view of the appropriate market price of an option will vary between market participants. So there won’t be standard price of the option.

Implied volatility: Implied volatility is the volatility implicit in the current option price, this is found by taking the current price of the option. When this volatility plugged into the option pricing then formula gives the current market price of the option. So it is useless.

Historical volatility: Historical volatility may be a useful measure for this purpose but it could prove to be defective as the past is not necessarily a good guide to the future. In addition, there are different ways to get the historical volatility like on the last month, the last three months, the last 6 months or last year, which one should be taken? The answer for this was the standardisation. The method used to calculate this is the annualized standard deviation of daily, weekly or even monthly changes in prices. The annualized price volatility is obtained by multiplying the calculated sample standard deviation by the number of periods. For daily data (based on 252 trading days per annum):

σ =  x daily standard deviation

for weekly data,

σ =  x weekly standard deviation

for monthly data,

σ =  x weekly standard deviation

 Futures Pricing Analysis  
  While futures market has a reputation for high risk and wild price swings, we cannot deny that prices vary suddenly and sharply. It is very difficult to measure the real price of the futures contract but it is quite possible to measure range of the non-arbitrage price with the theories that have been covered. Both the Cost-of-Carry and the Hedging Pressure Theory provide rational procedures for thinking about the behaviour of futures price. It must also be admitted that futures prices, on the whole, do not only conform to these theories there many other fundament, technical and psychological factors do have impact on the price with great extend.

After Analysising and researching on the theories, I found that some market follow more over to one particular theory. Below Table gives examples of which contract follow which market.

Capital Asset Pricing Model (CAPM) Theory

The Hedging Pressure Theory

The Cost of carry Model Theory


Example :



·        NASDAQ 100 Futures

·        Nikkei 225 Futures

·        S&P 500 Futures





·        Flaxseed WCE

·        Oats CBOT

·        Rice Rough

·        Soybeans e-cbot

·        Coffee

·        Coffee Mini

·        Orange Juice

·        Sugar #11






·        Gold

·        Silver

·        Eurodollar CME

·        Eurodollar GBX

·        T-Note 5

·          Yr CBOT

  Capital Asset Pricing Model (CAPM) is more suitable for the stock futures as the concept of capital asset pricing model is to measure and managing the systematic risk of the single stock/ a portfolio of stock in comparison with market portfolio. It is also handy with as Equity futures index as Equity futures index is a portfolio of many no. of shares.

The Hedging Pressure Theory is mostly used for market where futures price must consider convenience yield. The commodities contract on wheat, orange juice, Crude oil, soybean, corn, coco, coffee, meat which comes under the basic need of the human being can be valued very well with this theory. It is because this is the only theory that takes consideration of speculator’s point of view for coming in the market and taking the unwilling risk.

The Cost of carry Model is the widely used model all over the world for pricing financial instrument like futures contract, Interest rate contract, currency forward contracts stock futures contracts. It is most accurate on non-income generating storable assets like Gold, silver, platinum etc.
 Option Pricing Analysis  
  Option pricing is a relatively complex area. There are some crucial assumptions that need to be made for a valid application of the Black-Scholes pricing formula and Binomial pricing model. But I found that Binomial is more practical and has better predicting capability then Black-Scholes Model.  
  The Assumptions like stated below makes the Black-Scholes model weaker in terms of predicting the option price:  
  • Volatility: In the real market the market participant measures the volatility by strike price of the option, not by the statistical estimates so it varies from participant to participant.
• Continuous time: The model assumes continuous readjustments, but in practice traders can readjust only at discrete intervals.
• American Option: The formula we have looked at is only applicable to European options,
• Log-Normal Distribution: The formula assumes that the log of the share price follows a log-normal distribution. In the real world, distributions tend to have fatter tails than a normal distribution, meaning that there are better chances of an option being exercised that suggested by the Black-Scholes formula. Hence, in real world option prices are exceeding the Black-Scholes formula price.
  Binomial pricing model presents much greater transparency to the users of the Options prices. The Binomial Option has been able to leave some of these assumptions to get the realistic price of the Options. They are:  
  • Volatility:- The Upward/downward stock movements are governed by underlying asset’s volatility, and the model can use a term structure of volatility, a different volatility during each distinct measurement period (i.e. implied volatility during first 3 months and long-term volatility thereafter)
• Continuous time:- The Black-Scholes model assumes continuous readjustments, but in practice traders can readjust only at discrete intervals. The Binomial model calculates option values during each distinct measurement period the way calculated in real world.
• Risk-Free rate: The model can use different risk-free rate of return during each distinct measurement period.
  Because of these benefits the binomial model indeed give better result then Black-Scholes’ model, in fact the binomial model can also describe the insight of the Black-Scholes model. If we take n to infinity then the binomial model becomes more over same like black-Scholes’ model and results of that has same problem which we found in Black-scholes model.  
 Next Step  
  With the limitation of researching time and limitation of words, I was able to cover only the basics of the derivative markets.  
 Options Pricing  
  The next step towards analysis of the option pricing would be the consideration of the dividend in the stock market for stock option, Analysising the put call parity, Black-scholes model for American call, Uses of Greek letters and analysis of Option strategies for risk management and mathematic example for all the theories.  
 Futures Pricing  
  The next step toward analysis of the Futures/Forward contract pricing would be having more understanding of interest rate futures contacts, analysising changes in formulas of cost-of-carry model whilst interest rate changes frequently and mathematic example for all the theories.  
 Reuter 3000 Xtra  
  Because of unable to get the software called Reuter 3000 Xtra for real market quotes and news, it was difficult to explain the real market pricing. With the help of this software in depth real market price analysis and real market examples would have been possible.  
  John C. Hull (2004). Options Futures and Other Derivatives. (5th Ed.) Prentice-Hall of India.

Anthony Saunders and Marcia Millon Cornet. Financial Institutions Management. (4th Ed.) McGraw-Hill Irwin

Robert T Daigler, (1993). Financial futures markets: concepts, evidence, and applications HarperCollins College Publishers.

Clewlow, Les, Strickland, Chris, Enron Corp (2000). Energy derivatives: pricing and risk management Lacima

Robert W. Kolb (1997). Understanding futures markets. Blackwell.

Stein, Leon Jerome (1986) The economics of futures markets Blackwell.

Keith Pilbeam (1998), Finance & Financial Markets Macmillan

Robert T Daigler, (1994). Financial futures markets: concepts, evidence, and applications HarperCollins College Publishers.

David A. Dubofsky (1992) Options and Financial Futures Valuation and Uses, McGram-Hill, Inc.

John C. Cox, Stephen A. Ross, Mark Rubinstein (1979) , Option Pricing : A Simplified Approch Journal of Financial Economics

Thomas Bending 2002, Lectures notes STX 2210, Middlesex University

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Glass bangles are still preferred at traditional occasions

Bangles are made from plastic are inexpensive and slowly replacing those made by glass. Along with gold, glass bangles are considered a symbol of the well-being of her husband and sons in certain communities. Glass bangles are still preferred at traditional occasions such as marriages and on festivals.

Exquisite bangles are made of gold or silver and studded with precious diamonds for an enhanced appeal. These bangles are created in eye-catching and magnificent designs, earning the patronage of discerning clients, Bangles worldwide. This gold and silver jewellery from all parts of India draw the inspiration of patterns from flowers, leaves, fruits, fish, stars and the moon.

Gemstones are so durable

A few are mineraloids not true minerals and are including here: opal, amber, and moldavite. Foremost is durability - it must not easily corrode away, nor can it be brittle. It is so durable that nearly all of the gold ever mined is still in circulation or storage. In some cases, the names are true misnomers, such as Green Amethyst for prasiolite-a transparent green variety of quartz.

In most cases, these variety names are historical, as the gemstones were not recognized as being varieties of other minerals until well after the name was in common use such as aquamarine, emerald, and heliodor as varieties of beryl. And that is related to the third characteristic, ductility. You can see the options are endless and when you are commissioning a piece, why compromise a thing when you can choose!

Taking care of gemstones

Steam cleaning is quite effective but can result in thermal shock because of the often-quick temperature change. It can result in cracking because parts of the stone are forced to expand at different times. Most gemstones can be immersed in a solution of mild detergent and warm water.

Likewise with pearls; although soaking can result in discoloration, so this should always be avoided. After soaking for a few minutes, gently clean the stone with a soft brush. Pearls should be dried after cleaning, using a soft towel, and air-blown dry. Extra care should be taken to remove dirt from the bottom of the setting, a common place for build-up to occur.

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