Valuing American options in the presence of user-defined smiles and time-dependent volatility: scenario analysis, model stress and lower-bound pricing applications

Peter Jäckel, Riccardo Rebonato

Abstract

ABSTRACT

A method is presented for the valuation of American style options as a function of an exogenously assigned future implied volatility surface evolution. Subject to this specification, this is done independently of any assumptions about a stochastic process of the underlying asset. The scope and applicability of the method are analyzed in detail. The approach should have applications in risk management, and to estimate a tight lower bound price for the American option.