will receive less GBP after converting the into GBP. However, if the GBP weakens against the , then the UK firm receives more GBP. This uncertainty exposes the firm to FX risk. Assuming that the cash flow is certain, the firm can enter into a forward contract to deliver the in 90 days time, in exchange for GBP at the current forward rate. This forward contract is free, and, presuming the expected cash arrives, exactly matches the firm's exposure, perfectly hedging their FX risk. If the cash flow is uncertain, a forward FX contract exposes the firm to FX risk in the opposite direction, in the case that the expected USD cash is not received, typically making an option a better choice. Using options, the UK firm can purchase a GBP call/USD put option (the right to sell part or all of their expected income for pounds sterling at a predetermined rate), which: protects the GBP value that the firm expects in 90 days' time (presuming the cash is received) costs at most the option premium (unlike a forward, which can have unlimited losses) yields a profit if the expected cash is not received but FX rates move in its favor Valuation: the Garman–Kohlhagen model As in the Black–Scholes model for stock options and the Black model for certain interest rate options, the value of a European option on an FX rate is typically calculated by assuming that the rate follows a log-normal process. The earliest currency options pricing model was published by Biger and Hull, (Financial Management, spring 1983). The model preceded the Garman and Kolhagen's Model. In 1983 Garman and Kohlhagen extended the Black–Scholes model to cope with the presence of two interest rates (one for each currency). Suppose that is the risk-free interest rate to expiry of the domestic currency and is the foreign currency risk-free interest rate (where domestic currency is the currency in which we obtain the value of the option; the formula also requires that FX rates – both strike and current spot be quoted in terms of "units of domestic currency per unit of foreign currency"). The results are also in the same units and to be meaningful need to be converted into one of the currencies. Then the domestic currency value of a call option into the foreign currency is The value of a put option has value where : is the