Efficient valuation of barrier options under equity and interest rate risks

In this paper we study European and American equity derivatives with barrier features within a generic market model characterized by correlated equity and interest rate risk factors. First of all, we provide general algorithms to price discretely monitored European and American knock-in and knock-out options. Secondly, we adapt these techniques to a fairly general market model characterized by local volatility and a correlated mean-reverting process for the interest rate and the detail how to improve its efficiency. In particular, we discuss how to improve the precision of lattice-based pricing techniques in case of barrier options and we assess the computational efficiency of the proposed algorithms with respect to standard Monte Carlo-based approaches. Finally, we test our algorithms for two particular sets of barrier contracts retrieving also the optimal exercise policies of their American counterparts in the form of critical surfaces.