Foreign exchange option (Ofer Abarbanel online library)

In finance, a foreign exchange option (commonly shortened to just FX option or currency option) is a derivative financial instrument that gives the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified date.[1] See Foreign exchange derivative.

The foreign exchange options market is the deepest, largest and most liquid market for options of any kind. Most trading is over the counter (OTC) and is lightly regulated, but a fraction is traded on exchanges like the International Securities Exchange, Philadelphia Stock Exchange, or the Chicago Mercantile Exchange for options on futures contracts. The global market for exchange-traded currency options was notionally valued by the Bank for International Settlements at $158.3 trillion in 2005.[citation needed]

Example

For example, a GBPUSD contract could give the owner the right to sell £1,000,000 and buy $2,000,000 on December 31. In this case the pre-agreed exchange rate, or strike price, is 2.0000 USD per GBP (or GBP/USD 2.00 as it is typically quoted) and the notional amounts (notionals) are £1,000,000 and $2,000,000.

This type of contract is both a call on dollars and a put on sterling, and is typically called a GBPUSD put, as it is a put on the exchange rate; although it could equally be called a USDGBP call.

If the rate is lower than 2.0000 on December 31 (say 1.9000), meaning that the dollar is stronger and the pound is weaker, then the option is exercised, allowing the owner to sell GBP at 2.0000 and immediately buy it back in the spot market at 1.9000, making a profit of (2.0000 GBPUSD − 1.9000 GBPUSD) × 1,000,000 GBP = 100,000 USD in the process. If instead they take the profit in GBP (by selling the USD on the spot market) this amounts to 100,000 / 1.9000 = 52,632 GBP.

Terms

  • Call option – the right to buy an asset at a fixed date and price.
  • Put option – the right to sell an asset at a fixed date and price.
  • Foreign exchange option – the right to sell money in one currency and buy money in another currency at a fixed date and rate.
  • Strike price – the asset price at which the investor can exercise an option.
  • Spot price – the price of the asset at the time of the trade.
  • Forward price – the price of the asset for delivery at a future time.
  • Notional – the amount of each currency that the option allows the investor to sell or buy.
  • Ratio of notionals – the strike, not the current spotor forward.
  • Numéraire – the currency in which an asset is valued.
  • Non-linear payoff – the payoff for a straightforward FX option is linear in the underlying currency, denominating the payout in a given numéraire.
  • Change of numéraire – the implied volatility of an FX option depends on the numéraire of the purchaser, again because of the non-linearity of {\displaystyle x\mapsto 1/x}.
  • In the money – for a put option, this is when the current price is less than the strike price, and would thus generate a profit were it exercised; for a call option the situation is inverted.

Risk management

An earlier pricing model was published by Biger and Hull, Financial Management, spring 1983. The model preceded Garmam and Kolhagen Model. A wide range of techniques are in use for calculating the options risk exposure, or Greeks (as for example the Vanna-Volga method). Although the option prices produced by every model agree (with Garman–Kohlhagen), risk numbers can vary significantly depending on the assumptions used for the properties of spot price movements, volatility surface and interest rate curves.

After Garman–Kohlhagen, the most common models are SABR and local volatility[citation needed], although when agreeing risk numbers with a counterparty (e.g. for exchanging delta, or calculating the strike on a 25 delta option) Garman–Kohlhagen is always used.

References

  1. ^“Foreign Exchange (FX) Terminologies: Forward Deal and Options Deal” Published by the International Business Times AU on February 14, 2011.
  2. ^“British Pound (GBP) to Euro (EUR) exchange rate history”. www.exchangerates.org.uk. Retrieved 21 September 2016.
  3. ^“Currency options pricing explained”. www.derivativepricing.com. Retrieved 21 September 2016.

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Ofer Abarbanel online library

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