Parametrization of Correlations in Multi-Stochastic Volatility/Local-Stochastic Volatility Models

10 Pages Posted: 5 May 2020 Last revised: 8 May 2020

Date Written: October 4, 2019

Abstract

When designing multi-asset stochastic volatility (SV) or local-stochastic volatility (LSV) models, one of the main issues involves the construction of the global correlation matrix. Typically correlation matrices for each assets' degrees of freedom are set and the challenge is to build a global correlation matrix which at least recovers these individual correlation matrices, is positive, and is a smooth function of inputs, so that meaningful sensitivities can be calculated.

We present a general methodology for constructing such correlation matrices that uses few parameters, is based on correlations of physical observables, applies to both SVs and LSVs, and works regardless of the dimensionality of the single-asset SV/LSV model.

Keywords: Stochastic Volatility, Local Volatility, Multi-Asset, Correlation

JEL Classification: G13

Suggested Citation

Bergomi, Lorenzo, Parametrization of Correlations in Multi-Stochastic Volatility/Local-Stochastic Volatility Models (October 4, 2019). Available at SSRN: https://ssrn.com/abstract=3563431 or http://dx.doi.org/10.2139/ssrn.3563431

Lorenzo Bergomi (Contact Author)

Societe Generale ( email )

Paris-La Défense, Paris 92987
France

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
49
Abstract Views
175
PlumX Metrics