Option Pricing When Correlations are Stochastic: An Analytical Framework

25 Pages Posted: 24 Apr 2007

See all articles by José Da Fonseca

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

Claudio Tebaldi

Bocconi University - CAREFIN - Centre for Applied Research in Finance; Bocconi University - Department of Finance; Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research

Date Written: September 2006

Abstract

In this paper we develop a novel market model where asset variances-covariances evolve stochastically. In addition shocks on asset return dynamics are assumed to be linearly correlated with shocks driving the variance-covariance matrix.

Analytical tractability is preserved since the model is linear-affine and the conditional characteristic function can be determined explicitly.

Quite remarkably, the model provides prices of vanilla options consistent with the smile and skew effects observed, while making possible to detect and quantify the correlation risk in multiple asset derivatives like basket options. In particular it can reproduce the asymmetric conditional correlations effect documented in Ang and Chen (2002) for equity markets.

We exemplify analytical tractability providing explicit pricing formulas for rainbow Best-of options.

Keywords: Wishart processes, Best-of Basket option, Stochastic Correlation, FFT

JEL Classification: G12, G13

Suggested Citation

Da Fonseca, José and Grasselli, Martino and Tebaldi, Claudio, Option Pricing When Correlations are Stochastic: An Analytical Framework (September 2006). Available at SSRN: https://ssrn.com/abstract=982183 or http://dx.doi.org/10.2139/ssrn.982183

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law ( email )

3 Wakefield Street
Private Bag 92006
Auckland Central 1020
New Zealand
64 9 921 9999 5063 (Phone)

Martino Grasselli (Contact Author)

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

Claudio Tebaldi

Bocconi University - CAREFIN - Centre for Applied Research in Finance ( email )

Via Roentgen 1
Milan, 20136
Italy

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research ( email )

Via Roentgen 1
Milan, 20136
Italy

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