Determining what an option is worth at expiry is easy. It will reflect the money that could be realised by the holder of the option by exercising that option. If that is nothing, then that is the value of the option.

This then highlights further terminology that will prove useful:

Intrinsic Value: The amount of money, if any, that could currently be realised by exercising an option with a given strike price. A call option has a intrinsic value if its strike price is below the spot exchange rate. A put option has an intrinsic value if its strike price is above the spot exchange rate.

**In-The-Money:** This term is applied to an option that has intrinsic value.

**Out-Of-The-Money:** A call option is said to be "out-of-the-money" if the underlying spot exchange rate is currently less than the strike price of the option. A put option is said to be "out-of- the-money" if the underlying spot exchange rate is currently more than the strike price of the option. An option that is "out-of-the-money" at expiry will have no value, and the holder of the option will allow it to expire worthless.

**At-The-Money:** Means that the strike price and the spot exchange rate are the same. Like the "out-of-the- money" option, the holder would allow the option to expire.

The premium quoted for a particular option at a particular time represents a consensus of the option's current value which is comprised of two elements: intrinsic value and time value. Intrinsic value is simply the difference between the spot price and the strike price. A put option will have intrinsic value only when the spot price is below the strike price. A call option will have intrinsic value only when the spot price is above the strike price. Options, which have intrinsic value, are said to be "in-the-money."

Time value is more complex. When the price of a call or put option is greater than its intrinsic value, it is because it has time value. Time value is determined by five variables: the spot or underlying price, the expected volatility of the underlying currency, the exercise price, time to expiration, and the difference in the "risk-free" rate of interest that can be earned by the two currencies. Time value falls toward zero as the expiration date approaches. An option is said to be "out-of-the-money" if its price is comprised only of time value. A variety of complex option pricing models such as Black-Scholes and Cox-Rubinstein have been developed to determine option pricing. Another commonly used model for currency option valuation is the Garmen-Kohlhagen model. There are many texts available which cover the specifics of option pricing models in detail. Interest rate differentials between nations and temporary supply/demand imbalances can also have an effect on option premiums. In the final analysis, option prices (premiums) must be low enough to induce potential buyers to buy and high enough to induce potential option writers to sell.

While it is not necessary to understand the actual mathematics of the option-pricing model, it is useful to have some understanding of how the various components of the model affect the option premium.

The major inputs to models of this type are:

Current asset price

Exercise price

Time to expiry of option

Volatility

Risk-free money rate

Holding benefit or dividend rate on underlying instrument

Black and Scholes did the most famous option pricing theory work. Their work has been subsequently modified for valuing options in a number of markets (e.g. Garman-Kohlhagen for currencies, Black for futures, the Binomial model for American options). The basic idea of these models is to specify the condition that a dynamic hedge should be able to be created between an option and the underlying instrument, and then to use the fact that the resulting riskless portfolio should earn the risk-free rate. The solution to the equation specifying the condition, given the known boundary values of the option at expiry provides the fair value of the option at any time and the hedging mechanism required. It is assumed that the price of the underlying instrument follows some sort of stochastic process.

In fact, it is now widely recognised that these models have reasonable validity in the case of equities, currencies and commodities. The principal difficulties relate to the constant volatility and constant interest rate assumptions, and are especially significant for longer dated options. It is equally widely recognised that the models become increasingly shaky for interest rate options, especially long--dated ones. Certainly, the problems encountered for the other instruments are no less, but there is also a massive conceptual problem in assuming a constant money rate for the life of the option while at the same time using a stochastic process for the interest rate related instrument on which the option is written.

It is important to realise that the fair value of an option calculated according to a Black and Scholes type model only makes sense in the context of the riskless hedge argument. It is certainly possible to buy options under fair value, as determined by you, and to lose money; or to sell option above your fair value and lose money The only way the fair value can be locked in is by maintaining the dynamic hedge, either through the underlying instrument itself or by means of other suitable options in a portfolio approach. Even then, there is usually some degree of sensitivity to assumptions about the underlying stochastic process and its volatility.

A good starting point from which to understand the pricing of a currency option is to break the option premium down into two parts - its intrinsic value and its time value. For any option, the premium will be equal to the sum of its intrinsic value and its time value.

Traders adopt a variety of strategies in managing the risks in their portfolios. Generally, risk exposure is kept to an acceptable minimum by setting limits to losses given specified degrees of adverse market movements.

Broadly, the depth of the traders activity in the option market determines the profile of the risk exposure experienced. e.g. broking (avoiding open positions) or spread trading (limit loss potential) as opposed to market making. Risk is sensitive to the trader's own perception of market movement. A trader will decide when to buy or sell options (volatility positioning), when or how to hedge or when to close a position and take profit/cut losses.

The only perfect hedge for any specific option is the same option on the other side. However, such a strategy requires a large turnover and wide customer base to be profitable. Most market makers do not hedge options on an "option-for-option" basis as this is costly and is inefficient compared to a hedging strategy based on a portfolio approach.

This then highlights further terminology that will prove useful:

Intrinsic Value:

The premium quoted for a particular option at a particular time represents a consensus of the option's current value which is comprised of two elements: intrinsic value and time value. Intrinsic value is simply the difference between the spot price and the strike price. A put option will have intrinsic value only when the spot price is below the strike price. A call option will have intrinsic value only when the spot price is above the strike price. Options, which have intrinsic value, are said to be "in-the-money."

Time value is more complex. When the price of a call or put option is greater than its intrinsic value, it is because it has time value. Time value is determined by five variables: the spot or underlying price, the expected volatility of the underlying currency, the exercise price, time to expiration, and the difference in the "risk-free" rate of interest that can be earned by the two currencies. Time value falls toward zero as the expiration date approaches. An option is said to be "out-of-the-money" if its price is comprised only of time value. A variety of complex option pricing models such as Black-Scholes and Cox-Rubinstein have been developed to determine option pricing. Another commonly used model for currency option valuation is the Garmen-Kohlhagen model. There are many texts available which cover the specifics of option pricing models in detail. Interest rate differentials between nations and temporary supply/demand imbalances can also have an effect on option premiums. In the final analysis, option prices (premiums) must be low enough to induce potential buyers to buy and high enough to induce potential option writers to sell.

While it is not necessary to understand the actual mathematics of the option-pricing model, it is useful to have some understanding of how the various components of the model affect the option premium.

The major inputs to models of this type are:

Current asset price

Exercise price

Time to expiry of option

Volatility

Risk-free money rate

Holding benefit or dividend rate on underlying instrument

Black and Scholes did the most famous option pricing theory work. Their work has been subsequently modified for valuing options in a number of markets (e.g. Garman-Kohlhagen for currencies, Black for futures, the Binomial model for American options). The basic idea of these models is to specify the condition that a dynamic hedge should be able to be created between an option and the underlying instrument, and then to use the fact that the resulting riskless portfolio should earn the risk-free rate. The solution to the equation specifying the condition, given the known boundary values of the option at expiry provides the fair value of the option at any time and the hedging mechanism required. It is assumed that the price of the underlying instrument follows some sort of stochastic process.

In fact, it is now widely recognised that these models have reasonable validity in the case of equities, currencies and commodities. The principal difficulties relate to the constant volatility and constant interest rate assumptions, and are especially significant for longer dated options. It is equally widely recognised that the models become increasingly shaky for interest rate options, especially long--dated ones. Certainly, the problems encountered for the other instruments are no less, but there is also a massive conceptual problem in assuming a constant money rate for the life of the option while at the same time using a stochastic process for the interest rate related instrument on which the option is written.

It is important to realise that the fair value of an option calculated according to a Black and Scholes type model only makes sense in the context of the riskless hedge argument. It is certainly possible to buy options under fair value, as determined by you, and to lose money; or to sell option above your fair value and lose money The only way the fair value can be locked in is by maintaining the dynamic hedge, either through the underlying instrument itself or by means of other suitable options in a portfolio approach. Even then, there is usually some degree of sensitivity to assumptions about the underlying stochastic process and its volatility.

A good starting point from which to understand the pricing of a currency option is to break the option premium down into two parts - its intrinsic value and its time value. For any option, the premium will be equal to the sum of its intrinsic value and its time value.

Traders adopt a variety of strategies in managing the risks in their portfolios. Generally, risk exposure is kept to an acceptable minimum by setting limits to losses given specified degrees of adverse market movements.

Broadly, the depth of the traders activity in the option market determines the profile of the risk exposure experienced. e.g. broking (avoiding open positions) or spread trading (limit loss potential) as opposed to market making. Risk is sensitive to the trader's own perception of market movement. A trader will decide when to buy or sell options (volatility positioning), when or how to hedge or when to close a position and take profit/cut losses.

The only perfect hedge for any specific option is the same option on the other side. However, such a strategy requires a large turnover and wide customer base to be profitable. Most market makers do not hedge options on an "option-for-option" basis as this is costly and is inefficient compared to a hedging strategy based on a portfolio approach.

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