Lookback Call Option

A model is presented for pricing a European lookback call option on a stock index with guaranteed exchange rate (LBCGER). We define a lookback window . In addition a sampling frequency (e.g., daily, weekly, etc.) over the lookback window is specified.

Let delta denote the value at time t for the underlying security. The strike of the LBCGER, K , is set equal to the minimum price of the underlying security over a set of discrete points

The payoff at maturity is the value of a standard European call with strike adjusted by the guaranteed exchange rate

The method for pricing a lookback call option with guaranteed exchange rate is based on a single factor Monte Carlo approach. The idea of the method is to stochastically generate a large number of discrete sample paths for the underlying security.

Risk neutral pricing formulas are presented for various types of cross-currency instruments, in particular, European call options with payoffs at maturity of the form

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