On the use of the moment-matching technique for pricing and hedging multi-asset spread options

The aim of this paper is to show the benefit of applying a moment matching technique to the short leg component in order to price and hedge multi-asset spread options: in particular, we approximate the real dynamics of the short leg component by taking a log-normal proxy, whose equivalent volatility can be computed by performing a two-moment matching approximation. The pricing of the option is then performed once the equivalent correlation parameter between the long leg underlying and the proxy short leg component has been calculated. The main advantage associated with the moment matching approach proposed in this paper is a reduction of the dimension of the pricing problem: we can, indeed, continue using all the option formulas available in the literature for two-legged spread options, i.e. spread options written on two underlyings. Besides it, the combined use of an option formula for two-legged spread options and the moment matching technique applied to the short leg component provides a good approximation to the Monte Carlo simulation. It is well-known that the Monte Carlo price and Greeks can be considered as the benchmark since no exact formula is available for the pricing and hedging of multi-asset spread options. The accuracy of our approach is even comparable to the one provided by using closed form approximation formulas based on three underlyings, where each underlying entering into the short leg component is treated separately.