Valuation of exchange option with stochastic liquidity risk: a probabilistic approach

Abstract

We investigate a probabilistic approach for the valuation ofexchange option with stochastic liquidity risk. To measure market liquidityrisk, Ornstein-Uhlenbeck (OU) process with the mean reversion featureis used. A liquidity discount factor is applied to the underlying assets toallow for possible effects. We derive the characteristic function using aprobabilistic approach, and subsequently obtain the pricing formula forthe option using the measure change technique and the Fourier inversionformula.