European option pricing with market frictions, regime switches and model uncertainty

Abstract

The impact of market frictional costs on pricing insurance and financial products in a regime-switching environment has not been well-explored. This paper introduces a general pricing model for European options which incorporates market frictional costs, regime switches and model uncertainty. Regime switches are due to changes in an economic environment. Model uncertainty is attributed to misspecification of transition intensities for economic regimes. The selling and buying prices of a European option are determined through stochastic optimal control and nonlinear partial differential equations. A fair value is determined by a closed-form solution to a minimization problem based on a relative entropy. The fair value is consistent with the one obtained using the Esscher transform, which is an important tool in actuarial science. Numerical methods and results for implementing the pricing model are presented. The results indicate that after controlling for the model uncertainty, market frictional costs are more significant than regime switches in accounting for the fair, selling and buying prices.