Option Pricing in Multivariate Stochastic Volatility Models of OU Type

TL;DR

This paper introduces a flexible multivariate stochastic volatility model with leverage, enabling efficient multi-asset option pricing and covariance swap valuation, demonstrated through an OU-Wishart specification calibrated to currency options.

Contribution

The paper develops a new multivariate stochastic volatility model with analytical tractability, deriving characteristic functions and applying Fourier methods for multi-asset option pricing.

Findings

Model can be calibrated to market prices of currency options

Allows closed-form pricing of covariance swaps

Demonstrates efficiency of Fourier methods in multi-asset settings

Abstract

We present a multivariate stochastic volatility model with leverage, which is flexible enough to recapture the individual dynamics as well as the interdependencies between several assets while still being highly analytically tractable. First we derive the characteristic function and give conditions that ensure its analyticity and absolute integrability in some open complex strip around zero. Therefore we can use Fourier methods to compute the prices of multi-asset options efficiently. To show the applicability of our results, we propose a concrete specification, the OU-Wishart model, where the dynamics of each individual asset coincide with the popular Gamma-OU BNS model. This model can be well calibrated to market prices, which we illustrate with an example using options on the exchange rates of some major currencies. Finally, we show that covariance swaps can also be priced in closed form.