A closed-form formula for pricing exchange options with regime switching stochastic volatility and stochastic liquidity

Abstract

We propose a new framework for pricing exchange options, modeling two underlying assets of no liquidity issues with Heston stochastic volatility models adjusted for regime-switching long-run variance levels to capture economic cycles. Market liquidity, a stochastic factor affecting asset prices, is incorporated, leading to a discount in asset values. We then apply a regime-switching Esscher transform to establish a risk-neutral measure and analytically solve the partial differential equation for exchange option prices using dimension reduction and the Feynman–Kac theorem. This allows for numerical analysis of the market features’ impact on exchange option prices.