Black Basket Analytics for Mid-Curves and Spread-Options
20 Pages Posted: 30 Jun 2020 Last revised: 2 Nov 2020
Date Written: June 23, 2020
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.
Keywords: Spread options, mid curve, Copula, correlation freedom
JEL Classification: C1, C3, C5, C6, E43, G12, G13
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