Currency Options Price Dynamics

Determining what an option is worth at expiry is easy. It will reflect the money that could be realized by the holder of the option by exercising that option. If that is nothing, then that is the value of the option.
  
Intrinsic Value: The amount of money, if any, that could currently be realized 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.
  
In every foreign exchange transaction, one currency is purchased and another currency is sold. Consequently, every currency option is both a call and a put.
An option to buy Euros against GB POUND is both an Euro call and a GB POUND put. Conversely, an option to sell Euros against GB POUND  is an Euro put and GB POUND dollar call.
  
Lets take the example, where an EUROPEAN importer has the obligation in three months time to pay GBP1,000,000 for a commodity such as soymeal. The importer has a number of alternatives.
  
  a) Remain unhedged and purchase the GBP at the prevailing spot rate in three months time.
  
  b) Hedging by buying GBP forward;
  
  c) Hedging by using an options strategy
  
One of the many strategies available to an importer is to buy Euro put /GBPcall option.
  
The effect of buying an Euro put is to place a ceiling on the cost of imports without limiting the potential benefit if the spot rate rises. The importer limits the cost to a maximum whilst not limiting the minimum.
  
An exporter who will be receiving GBP1,000,000 in three months time as payment for a commodity has a number of alternatives.
  
  a) Remain unhedged and sell the GBP at the prevailing spot rate in three months time.
  
  b) Hedging by selling GBP forward;
  
  c) Hedging by using an options strategy
  
One of the many strategies available to an exporter is to buy an Euro call/GBP put option.
  
The effect of buying an Euro put is to guarantee a minimum payment for the export, whilst not limiting potential gains should the spot rate fall.
  
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.
  
Trading & Speculation
Currency options offer some unique features to the speculator. Purchasing an option you know that your downside is limited to the premium you invest. Sounds great and it is. However you should also know that the probability of make a profit is depending on where the option strike is. If GBP/JPY spot is 120.00 and you buy a 1 month 140.00 strike GBP Call, the premium will be small but the probability of losing it all is very high. On the other hand if you sell options you receive premium but you also are exposed to unlimited loss if the market moves against your position.

Hedging With Options
Options offer some very interesting features for hedging. There are a wide variety of different types of options to match the full spectrum of risks that companies and fund managers inherit as part of their international trade and investment.
  
If it important that risk managers understand the products they are buying and exactly how they perform under different scenarios. The goal being to negate the existing risks of the business.An option is said to have intrinsic value where the strike price of the option is more favourable than the current market forward rate.
  
As a general rule, the greater the intrinsic value of an option the higher its premium.An option with some intrinsic value is described as being "in-the-money".
An option with no intrinsic value is said to be "out-of-the-money".Where the strike price of the option is equal to the current forward rate the option is said to be "at-the-money".

Time Value (extrinsic)
The premium of an option that has no intrinsic value is made up solely of time value. Time value reflects the uncertainty of an option being exercised at expiry.
  
The time value of an option is a function of:
The relationship between the strike of the option and the current market forward rate
The time period of the option
The interest rate differential

The expected volatility in the underlying currency-pair
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1. Relationship between strike and current market forward rate
The time value of an option will be at a maximum when the strike price of an option is equal to the current forward rate. At that point, the degree of uncertainty surrounding whether or not the option will be exercised will be at its highest level.
  
As an option moves further "into the money" the time value of the option will fall as the probability of it being exercised increases. Similarly, if the option moves further  "out-of-the-money" the time value of the option will also fall as the probability of it not being exercised increases.
  
2. Time Period
In general, the longer the period of an option, the greater its potential pay-off and therefore the more expensive it will be. While the amount of time value of an option will increase as the maturity lengthens it will do so at a decreasing rate.
  
3. Interest Rate Differentials
The interest rate differential between the two currencies in any particular option affects the option premium by affecting the relationship between the strike of the option and the current market forward rate. Any movement in the interest rate differential that shifts the underlying option further in-the-money will make the option more expensive; any movement that shifts it further out-of-the-money will make it cheaper.

4. Volatility
The expected volatility in the underlying exchange rate is the most important variable in pricing a currency option. The higher the volatility the greater the potential for large exchange rate movements and hence the greater the potential pay-off of an option. Consequently, higher volatility will translate into higher premiums for both puts and calls.

Option traders often differ in their expectations of future volatility. Influencing a traders expectations will be the historical volatility of the particular currency pair (i.e. its recent track record), the potential impact of future news and data releases on the currency, the relative demand for options, other traders expectations and any other factors that the trader feels could materially affect future movements in the currency.