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

Suggested Citation

Antonov, Alexandre, Black Basket Analytics for Mid-Curves and Spread-Options (June 23, 2020). Available at SSRN: or

Alexandre Antonov (Contact Author)

Danske Bank - Danske Markets ( email )

Holmens Kanal 2-12
DK-1092 Copenhagen K

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