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Control variates and conditional Monte Carlo for basket and Asian options

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  • Dingeç, Kemal Dinçer
  • Hörmann, Wolfgang

Abstract

A new, very efficient and fairly simple simulation method for European basket and Asian options under the geometric Brownian motion assumption is presented. It is based on a new control variate method that uses the closed form of the expected payoff conditional on the assumption that the geometric average of all prices is larger than the strike price. The combination of that new control variate with conditional Monte Carlo and quadratic control variates leads to the newly proposed algorithm. Numerical experiments show that the new algorithm is more efficient than the classical control variate method using the geometric price.

Suggested Citation

  • Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2013. "Control variates and conditional Monte Carlo for basket and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 421-434.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:3:p:421-434
    DOI: 10.1016/j.insmatheco.2013.03.002
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    Citations

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    Cited by:

    1. Shiraya, Kenichiro & Takahashi, Akihiko, 2017. "A general control variate method for multi-dimensional SDEs: An application to multi-asset options under local stochastic volatility with jumps models in finance," European Journal of Operational Research, Elsevier, vol. 258(1), pages 358-371.
    2. Yijuan Liang & Xiuchuan Xu, 2019. "Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities," Sustainability, MDPI, vol. 11(3), pages 1-21, February.
    3. Geon Ho Choe & Minseok Kim, 2021. "Closed‐form lower bounds for the price of arithmetic average Asian options by multiple conditioning," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(12), pages 1916-1932, December.
    4. Kenichiro Shiraya & Akihiko Takahashi, 2016. "A General Control Variate Method for Multi-dimensional SDEs: An Application to Multi-asset Options under Local Stochastic Volatility with Jumps Models in Finance (Subsequently published in "Europ," CARF F-Series CARF-F-382, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2016.
    5. Kenichiro Shiraya & Akihiko Takahashi, 2016. "A General Control Variate Method for Multi-dimensional SDEs: An Application to Multi-asset Options under Local Stochastic Volatility with Jumps Models in Finance," CIRJE F-Series CIRJE-F-1007, CIRJE, Faculty of Economics, University of Tokyo.
    6. Ortiz-Gracia, Luis, 2020. "Expected shortfall computation with multiple control variates," Applied Mathematics and Computation, Elsevier, vol. 373(C).

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    More about this item

    Keywords

    Basket options; Asian options; Monte Carlo simulation; Control variate; Conditional Monte Carlo;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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