Option pricing when correlations are stochastic: An analytical framework

被引：0
作者：
Da Fonseca J. [1 ,2 ]
Grasselli M. [1 ,3 ]
Tebaldi C. [4 ,5 ]
机构：
[1] Ecole Supérieure d'Ingénieurs Léonard de Vinci, Departement Mathématiques et Ingénierie Financière
[2] Zeliade Systems, Paris 75001, 56, Rue Jean-Jacques Rousseau
[3] Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Padova
[4] IMQ, Università Bocconi Milano, Milano 20139
[5] Università degli Studi di Verona, Verona
来源：
Review of Derivatives Research | 2007年 / 10卷 / 2期
关键词：
Best-of basket option; FFT; Stochastic correlation; Wishart processes;
D O I：
10.1007/s11147-008-9018-x
中图分类号：
学科分类号：
摘要：
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 for vanilla options consistent with observed smile and skew effects, while making it possible to detect and quantify the correlation risk in multiple-asset derivatives like basket options. In particular, it can reproduce and quantify the asymmetric conditional correlations observed on historical data for equity markets. As an illustrative example, we provide explicit pricing formulas for rainbow "Best-of" options. © 2008 Springer Science+Business Media, LLC.
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页码：151 / 180
页数：29
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