Closed-Form Pricing of Two-Asset Barrier Options with Stochastic Covariance

Abstract

Single and double barrier options on more than one underlying with stochastic volatility are usually priced via Monte Carlo simulation due to the non-existence of closed-form solutions for their value. In this paper, for a special dependence structure, the prices of some two-asset barrier derivatives, like double-digital options and correlation options can be derived analytically using generalized Fourier transforms and some conditions on the characteristic functions. We study the influence of the various parameters on these prices and show that these formulas can be easily and quickly computed. We also extend our approach to further allow for a random correlation structure.

Key Words:

• Stochastic volatility
• random correlation
• generalized Fourier transform
• barrier options