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FX Options

Introduction

Foreign exchange options are an alternative to forward contracts when hedging an FX exposure because options allow the company to benefit from favorable FX rate movements, while a forward contract locks in the FX rate for a future transaction. Of course this "insurance" from the option is not free, while it costs nothing to enter into a forward transaction.

When pricing foreign exchange options, the underlying is the spot or forward foreign exchange rate.

Settlement convention refers to the potential time lag that occurs between the trade and settlement dates. Financial contracts generally have a delay between the execution of a trade and its settlement. This time period is also present between the expiry of an option and its settlement. For example, for an FX forward against USD, the standard date calculation for spot settlement is two business days in the non-dollar currency, and then the first good business day that is common to the currency and New York. The only exception to this convention is USD-CAD which is one Toronto business day, and then the first common business day in Toronto and New York. For an FX option, cash settlement is made in the same manner, with the settlement calculation using the option expiry date as the start of the calculation. The settlement convention affects discounting cash flows and must be considered in the valuation. The FINCAD functions allow the specification of various FX rate market conventions that are able to cover most currency pairs available in the market. Regarding the possible input formats, the users can specify the conventions for the two currencies of the FX rate manually, in a combined or separate manner. For the former, two elements can be taken in as maturity descriptor and holiday convention that are shared for both currencies. For the latter, five elements can be taken in as one set of maturity descriptor and holiday convention for the currency one, another set of similar inputs for the currency two and an additional input of holiday convention. This corresponds to the most generic specification of the settlement convention that can be used for cross rate trades, e.g. a CAD-EUR trade that has settlement dates calculated using New York as well as Toronto and Target holidays.

If we assume that exchange rates follow geometric Brownian motion (same type of stochastic process as a stock), using USD / JPY as the FX rate, the foreign currency (JPY) is analogous to a stock providing a known dividend yield, where the owner of the foreign currency receives a "dividend yield" equal to the risk-free rate in the foreign currency. These and other assumptions allow us to utilize generic option models, such as Black-Scholes, in the valuation of FX options.

Technical Details

FX options can be confusing and sometimes require a little extra thought because one customer will consider the option a CALL and another will consider the same FX option a PUT. It is always important to understand what the expected payoff is because once the payoff is known the inputs to the option functions will be clear.

As an example, if the strike rate is 1.45 CAD/USD ($1.45 CAD buys $1.00 USD) then the payoff for a long call on USD would look like the illustration below. Remember that a call on USD is the same as a put on CAD, so if the CAD/USD rate rises to 1.50, a 1.45 PUT on CAD is in the money.

Payoff for a Long Call on USD


Analysis Supported

FINCAD FX options functions can be used for the following:

  • Calculate fair value and risk statistics for a European, American or Asian FX option;
  • Calculate fair value, risk statistics and risk report of a European FX option with settlement convention;
  • Calculate fair value and risk statistics for a European or American exercise single barrier FX option;
  • Calculate fair value and risk statistics for a European or American exercise double barrier FX option. The option is a double knock-out barrier option, and the payoff may be vanilla or binary type: initially the holder owns a call or put binary option, but if at any time either barrier is breached, the option is lost or knocked-out;
  • Calculate fair value and risk statistics for a binary FX option
  • Calculate fair value and risk statistics for a binary barrier FX option. The payoff is a fixed amount of cash if the barrier is breached; otherwise, nothing if the barrier is never breached, and vise versa;
  • Calculate fair value and risk statistics for a binary barrier FX option. The payoff is a fixed amount of cash if the barrier is touched and the option is in the money at expiry; otherwise, nothing;
  • Calculate fair value and risk statistics for a binary barrier FX option. The payoff is a fixed amount of cash if the barrier is not touched and the option is in the money at expiry; otherwise, nothing.

To learn more about FINCAD FX options functions, contact a FINCAD Representative

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