Time-dependent principal components-based dimension reduction in multi-dimensional foreign exchange option pricing

Abstract

I apply a principal components-based dimension reduction technique to foreign exchange (FX) basket option pricing. The underlying FX rates are modeled by the Black-Scholes model extended with Hull-White stochastic interest rates. A full correlation structure between the underlyings is included. The dimension of the model is fi?rst reduced by switching to the domestic forward measure. Second, the FX basket option pricing problem is rewritten in terms of the principal components of the forward FX rates. Further dimension reduction is then achieved by substituting all except for a few principal components with large variance by their expected value. I contribute to the existing literature by including the time-dependence of the principal components composition in high-dimensional option pricing. Real market data is used to calibrate the model to several emerging and nonemerging market currencies. In line with expectations, the accuracy of the dimension reduction technique depends on the correlation between the currencies: more accurate results are obtained for higher correlation values.