Efficient Valuation of Barrier Options under Equity and Interest Rate Risks

Abstract

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 and continuously monitored European and American knock-in and knock-out options. Then, we adapt these techniques to a fairly general market model characterized by local volatility and a correlated mean-reverting process with no zero lower bound for the interest rate. Finally, we test our algorithms for two particular sets of barrier contracts, across a positive and a negative/zero interest rate environments, studying the determinants of the contracts' fair values and retrieving the optimal exercise policies of their American counterparts in the form of critical surfaces.

Keywords: mathematical finance, derivatives pricing, barrier options, interest rate risk, American options.

JEL Classification: G13