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

Nicola Cufaro Petroni () and Piergiacomo Sabino ()
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Nicola Cufaro Petroni: Università di Bari, INFN Sezione di Bari
Piergiacomo Sabino: Università di Bari

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 1, 147-163

Abstract: 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).

Keywords: Computational finance; Quasi-Monte Carlo algorithms; Malliavin Calculus; Pricing and hedging options; Asian basket options; 91G60 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-011-9228-9

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