Black Basket Analytics for Mid-Curves and Spread-Options

Abstract

To price mid-curve or spread options we need flexible joint distributions of two underlying rates with fixed marginals. A Copula approach is a standard method to produce such joint distributions.It has, however, several drawbacks, especially, a low number of free parameters. For example, the most popular Gaussian copula has one parameter -- correlation. Another complication with the Copulas is its numerical realization: a two dimensional numerical integration underlying the price can be slow and potentially noisy, eps. for sensitivities. In this paper we propose a new way to unify two marginal distributions such that it has a large number of parameters permitting to calibrate to mid-curve or spread options with multiple strikes. The method is based on a basket of log-normal processes (called Black Basket) having a fast analytical formulation and attractive simplicity.