Currency-translated Foreign Equity Options with Path Dependent Features and Their Multi-asset Extensions

Currency-translated foreign equity options (quanto options) are designed for investors who would like to manage different types of risk in international equity investments. The terminal payoffs of quanto options depend on the price of a foreign currency denominated asset (or stock index) and the exchange rate in different combinations of choices. This paper presents a systematic framework to derive pricing formulas for different European-style quanto options with path-dependent payoff functions. The path dependent features can be the barrier feature associated with the underlying asset price movement, the averaging feature of the exchange rate over the life of the option, etc. In many cases, the pricing formulas for quanto options can be inferred from their vanilla counterparts by applying the quanto-prewashing technique of making modifications on the risk neutralized drift rates and volatility rates. The extension of the pricing formulations to multi-asset extremum options with the quanto feature is also considered. The pricing behaviors of the joint quanto options and the Asian quanto options are examined.