Pricing Path-dependent Options in Some Black-scholes Market, from the Distribution of Homogeneous Brownian Functionals
نویسنده
چکیده
We give some explicit formulae for the prices of two path-dependent options which combine Brownian averages and penalizations. Because these options are based on both the maximum and local time of Brownian motion, the obtention of their prices necessitates some involved study of homogeneous Brownian functionals, which may be of interest by themselves. 1. Motivation, introduction 1.1. To (Bt, t ≥ 0), a one-dimensional Brownian motion, we associate its maximum, minimum and local time processes, which we denote respectively by: Mt = sup s≤t Bs, It = inf s≤t Bs, Lt = lim ε→0 1 2ε ∫ t
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