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Proxy simulation schemes using likelihood ratio weighted Monte Carlo for generic robust Monte-Carlo sensitivities and high accuracy drift approximation (with applications to the LIBOR Market Model)

Author

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  • Christian P. Fries

    (Universität Heidelberg)

  • Joerg Kampen

    (Universität Heidelberg)

Abstract

We consider a generic framework for generating likelihood ratio weighted Monte Carlo simulation paths, where we use one simulation scheme K° (proxy scheme) to generate realizations and then reinterpret them as realizations of another scheme K* (target scheme) by adjusting measure (via likelihood ratio) to match the distribution of K° such that E( f(K*) | F_t ) = E( f(K°) w | F_t ). This is done numerically in every time step, on every path. This makes the approach independent of the product (the function f) and even of the model, it only depends on the numerical scheme. The approach is essentially a numerical version of the likelihood ratio method [Broadie & Glasserman, 1996] and Malliavin's Calculus [Fournie et al., 1999; Malliavin, 1997] reconsidered on the level of the discrete numerical simulation scheme. Since the numerical scheme represents a time discrete stochastic process sampled on a discrete probability space the essence of the method may be motivated without a deeper mathematical understanding of the time continuous theory (e.g. Malliavin's Calculus). The framework is completely generic and may be used for high accuracy drift approximations and the robust calculation of partial derivatives of expectations w.r.t. model parameters (i.e. sensitivities, aka. Greeks) by applying finite differences by reevaluating the expectation with a model with shifted parameters. We present numerical results using a Monte-Carlo simulation of the LIBOR Market Model for benchmarking.

Suggested Citation

  • Christian P. Fries & Joerg Kampen, 2005. "Proxy simulation schemes using likelihood ratio weighted Monte Carlo for generic robust Monte-Carlo sensitivities and high accuracy drift approximation (with applications to the LIBOR Market Model)," Finance 0504010, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpfi:0504010
    Note: Type of Document - pdf; pages: 27
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0504/0504010.pdf
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    References listed on IDEAS

    as
    1. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Monte-Carlo; Likelihood Ratio; Malliavin Calculus; Sensitivities; Greeks;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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