FX Options and Smile Risk

5

Plain Vanilla Options

5.1 PRICING OF PLAIN VANILLA OPTIONS

The pricing of FX plain vanilla options has already been dealt with in Chapter 2, where we sketched the basic features of several models and provided the pricing formulae to evaluate (base currency) call and put options in each of their frameworks. We then referred to other chapters for the details. Here we would just like to stress that the interbank market reference is the BS model, since quoted implied volatilities are relative to this model and also Delta amounts are calculated by the same model. After a deal is struck, the premium (expressed according to the market conventions for the underlying pair) is calculated by the BS formula with the FX spot rate and the interest rates, for the two currencies involved, prevailing in the market, and the agreed implied volatility.

5.1.1 Delayed settlement date

Plain vanilla options are written on the spot FX rate: at expiry the buyer of the option can exercise the right to enter into a spot transaction to buy or sell the notional amount of base currency against the numeraire currency at the strike price. The settlement of this transaction is regulated according to the rules we examined in Chapter 1. Nonetheless, two counterparties may agree to settle the transaction at a different date, for example one month later than the expiry date. In this case the pricing of the option has to take that into account.

While the standard options pricing formulae we have examined up ...