Functionals of Brownian Motion in Path-Dependent Option Valuation

  • Hélyette Geman
Part of the Progress in Mathematics book series (PM, volume 202)


Path-dependent options have become increasingly popular over the last few years, in particular in FX markets, because of the greater precision with which they allow investors to choose or avoid exposure to well-defined sources of risk. The goal of the paper is to exhibit the power of stochastic time changes and Laplace transform techniques in the evaluation and hedging of path-dependent options in the Black-Scholes-Merton setting. We illustrate these properties in the specific case of Asian options and continuously (de)activating double-barrier options and show that in both cases, the pricing, and as importantly, the hedging results are more accurate than the ones obtained through Monte Carlo simulations.


Brownian Motion Asset Price Option Price Geometric Brownian Motion Underlying Asset 
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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Hélyette Geman
    • 1
    • 2
  1. 1.Securities Markets, Commodities Markets and Risk ManagementUniversité de Paris IX DauphineParis cedex 16France
  2. 2.ESSEC Graduate Business SchoolFrance

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