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Test of Log-Normal Process with Importance Sampling for Options Pricing

Author

Listed:
  • Semih Yon

    (Istanbul Technical University)

  • Cafer Erhan Bozdag

    (Istanbul Technical University)

Abstract

Log-normal process and martingale restriction bring some bias on the premium for option pricing models. It is possible to reduce the bias by adding more parameters like jump diffusion, stochastic volatility or regime switching. In this case closed form solutions and numerical approximations suffer from the dimension of the problem. Monte Carlo integration then appears to be unique solution for high dimensional calculations. However variance of the output of interest should be decreased in Monte Carlo applications in order to have confident results. The method of Importance Sampling can be used in an attempt to reduce variance. In this study we test the log-normal process for options pricing via Importance Sampling Monte Carlo. Our analysis is based on the theory of variance reduction and we don?t have any empirical data. Numerical results indicate that the risk neutral density should be substituted in the range of moneyness.

Suggested Citation

  • Semih Yon & Cafer Erhan Bozdag, 2014. "Test of Log-Normal Process with Importance Sampling for Options Pricing," Proceedings of Economics and Finance Conferences 0401571, International Institute of Social and Economic Sciences.
    • Handle: RePEc:sek:iefpro:0401571
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    File URL: https://iises.net/proceedings/2nd-economics-finance-conference-vienna/table-of-content/detail?cid=4&iid=33&rid=1571
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    References listed on IDEAS

    as
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    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    More about this item

    Keywords

    Options pricing; lognormal process; variance reduction; importance sampling; moneyness;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G00 - Financial Economics - - General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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