Pricing Barriers on Underlyings with Time-Dependent Parameters

Abstract

The purpose of this note is to explain the technique and the results obtained by C.F.Lo et al. in their papers on the pricing of barriers on underlyings whose evolution is given by the Black-Scholes model with time-dependent parameters, with formulae that cover (almost) fully the profusion of barrier options traded on the market.

Keywords: option pricing, barrier options, Black-Scholes, partial differential equations, diffusion equation, boundary problems, FX derivatives, credit derivatives