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Time-dependent barrier options and boundary crossing probabilities. (English) Zbl 1060.91067
Summary: 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 nonlinear 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.

91B28 Finance etc. (MSC2000)
60J65 Brownian motion
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