Pricing of spread options on stochastically correlated underlyings

Abstract

This paper proposes a method to price spread options on stochastically correlated underlying assets. Therefore, it provides a more realistic approach towards a dependence structure. We generalize a constant correlation tree algorithm developed by Hull (2002) and extend it using the notion of stochastic correlation. The resulting tree algorithm is recombining and easy to implement. Moreover, the average price error decreases approximately as n−1.6, where n is the number of time steps. We show that this level of convergence is similar to that of the algorithm for the constant correlation case. Our sensitivity analysis with respect to the stochastic correlation parameters shows that the constant correlation model systematically overprices spread options on two stochastically correlated underlying assets. Furthermore, we use our model to derive hedge ratios for the correlation of a spread option and show that the constant correlation model also overprices the hedge ratios.