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Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations

Author

Listed:
  • Nicola Cufaro Petroni

    (Università di Bari, INFN Sezione di Bari)

  • Piergiacomo Sabino

    (Università di Bari
    E.ON Energy Trading SE)

Abstract

In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulations. We assume a Black–Scholes market with time-dependent volatilities, and we compute the deltas by means of the Malliavin Calculus as an extension of the procedures employed by Kohatsu-Higa and Montero (Physica A 320:548–570, 2003). Efficient path-generation algorithms, such as Linear Transformation and Principal Component Analysis, exhibit a high computational cost in a market with time-dependent volatilities. To face this challenge we then introduce a new and faster Cholesky algorithm for block matrices that makes the Linear Transformation more convenient. We also propose a new-path generation technique based on a Kronecker Product Approximation. Our procedure shows the same accuracy as the Linear Transformation used for the computation of deltas and prices in the case of correlated asset returns, while requiring a shorter computational time. All these techniques can be easily employed for stochastic volatility models based on the mixture of multi-dimensional dynamics introduced by Brigo et al. (2004a, Risk 17(5):97–101, b).

Suggested Citation

  • Nicola Cufaro Petroni & Piergiacomo Sabino, 2013. "Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 147-163, March.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:1:d:10.1007_s11009-011-9228-9
    DOI: 10.1007/s11009-011-9228-9
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    References listed on IDEAS

    as
    1. Piergiacomo Sabino, 2011. "Implementing quasi-Monte Carlo simulations with linear transformations," Computational Management Science, Springer, vol. 8(1), pages 51-74, April.
    2. Xiaoqun Wang, 2009. "Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 488-504, August.
    3. Montero, Miquel & Kohatsu-Higa, Arturo, 2003. "Malliavin Calculus applied to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 548-570.
    4. 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.
    5. Spassimir H. Paskov & Joseph F. Traub, 1995. "Faster Valuation of Financial Derivatives," Working Papers 95-03-034, Santa Fe Institute.
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