Expansion formulas for bivariate payoffs with application to best-of options on equity and inflation

A wide class of hybrid products are evaluated with a model where one of the underlying price follows a local volatility diffusion and the other asset value a log-normal process. Because of the generality for the local volatility function, the numerical pricing is usually much time consuming. Using proxy approximations related to log-normal modeling, we derive approximation formulas of Black-Scholes type for the price, that have the advantage of giving very rapid numerical procedures. This derivation is illustrated with the best-of option between equity and inflation where the stock price follows a local volatility model and the inflation rate a Hull-White process. The approximations possibly account for Gaussian HJM (Heath-Jarrow-Morton) models for interest rates. The experiments show an excellent accuracy.