The Valuation of Multiple Options: An Application to the Exchange Rate Market of the Italian Lira

The first part of the paper presents some basic relationships linking multiple options, i.e. options written on several risky assets and, specifically, options on the maximum and the minimum of n assets. This is followed by a description of the features of currency option bonds, which offer their holders a series of multiple currency options, and of the Fong and Vasicek M.A.P. strategy, which consists in replicating the payoff of a call option on the maximum written on several assets. Subsequently, Johnson’s equation for pricing options on the maximum of n assets is presented and adapted to the case of currency options, with a test of the underlying assumptions to see whether they apply to the exchange market of the lira. Call options on the maximum written on the dollar, the yen and the DM are then priced and a simulation carried out to replicate the value of these options with a dynamically adjusted portfolio made up of the three underlying currencies. Lastly, a comparison is made of the results obtained by an equally distributed multicurrency portfolio and by a M.A.P. strategy.