Skew-Brownian motion and pricing European exchange options br

This article derives a closed-form pricing formula for European exchange options under a non-Gaussianframework for the underlying assets, intending to resolve mispricing associated with a geometric Brownianmotion. The dynamics of each of the two correlated underlying assets are assumed to be governed by theexponential of a skew-Brownian motion, which is specified as a sum of a standard Brownian motion and anindependent reflected Brownian motion. The proposed pricing formula does not incur additional computationalcosts than the standard Black-Scholes framework, which one can quickly recover as a particular case of theproposed framework. Finally, we present some numerical experiments followed by a valuable discussion onthe result