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Jacques Tempere

  1. Path integral approach to Asian options in the Black-Scholes model.

    Mon, 09/26/2011 - 15:01 — SomNambul
    Authors: Damiaan Lemmens, Jacques Tempere, Jeroen P.A. Devreese
    Subjects: Pricing of Securities
    Abstract

    We derive a closed-form solution for the price of an average price as well as
    an average strike geometric Asian option, by making use of the path integral
    formulation. Our results are compared to a numerical Monte Carlo simulation. We
    also develop a pricing formula for an Asian option with a barrier on a control
    process, combining the method of images with a partitioning of the set of paths
    according to the average along the path. This formula is exact when the
    correlation is zero, and is approximate when the correlation increases.

  2. Path integral approach to the pricing of timer options with the Duru-Kleinert time transformation.

    Thu, 01/20/2011 - 16:01 — SomNambul
    Authors: Ling Zhi Liang, Damiaan Lemmens, Jacques Tempere
    Subjects: Pricing of Securities
    Abstract

    In this paper, a time substitution as used by Duru and Kleinert in their
    treatment of the hydrogen atom with path integrals is performed to price timer
    options under stochastic volatility models. We present general pricing formulas
    for both the perpetual timer call options and the finite time-horizon timer
    call options. These general results allow us to find closed-form pricing
    formulas for both the perpetual and the finite time-horizon timer options under
    the 3/2 stochastic volatility model as well as under the Heston stochastic
    volatility model.

Math-arch

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