Perturbed Copula: Introducing the skew effect in the co-dependence

TL;DR

This paper introduces a perturbed Gaussian copula that incorporates skew effects into the dependence structure between variables, enhancing modeling accuracy for derivative valuation, especially FX quanto options.

Contribution

The paper derives an analytical form of the perturbed copula using asymptotic expansion and applies it to derivative pricing, including a calibration method for skew.

Findings

Perturbed copula captures skew effects more effectively than Gaussian copula.

Application to FX quanto options shows improved pricing accuracy.

Comparison with local volatility models demonstrates the perturbed copula's advantages.

Abstract

Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both random variables into the co-dependence structure. The analytical expression of this copula is derived through an asymptotic expansion under the assumption of a common fast mean reverting stochastic volatility factor. This paper applies this new perturbed copula to the valuation of derivative products; in particular FX quanto options to a third currency. A calibration procedure to fit the skew of both underlying securities is presented. The action of the perturbed copula is interpreted compared to the Gaussian copula. A real worked example is carried out comparing both copulas and a local volatility model with constant correlation for varying maturities, correlations and skew configurations.