Time-Dependent Barrier Options and Boundary Crossing Probabilities

Alexander A. Novikov · Volf Frishling · Nino Kordzakhia

29 citations0/0 files storedGeorgian Mathematical Journal

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Stochastic processes and financial applications Probability and Statistical Research Probability and Risk Models

Abstract

Abstract The problem of pricing of time-dependent barrier options is considered in the case when interest rate and volatility are given functions in Black–Scholes framework. The calculation of the fair price reduces to the calculation of non-linear boundary crossing probabilities for a standard Brownian motion. The proposed method is based on a piecewise-linear approximation for the boundary and repeated integration. The numerical example provided draws attention to the performance of suggested method in comparison to some alternatives.

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1994Option pricing: Mathematical models and computation 1997Financial Calculus: An Introduction to Derivative Pricing.2000ESSENTIALS OF STOCHASTIC FINANCE 1997Boundary crossing probability for Brownian motion and general boundaries 2001Boundary crossing probability for Brownian motion 1999Approximations of boundary crossing probabilities for a Brownian motion 1997Pricing Barrier Options with Time–Dependent Coefficients 1992A general nonstationary diffusion model for two-choice decision-making

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