BRANCHING PARTICLE PRICERS WITH HESTON EXAMPLES

Michael A. Kouritzin () and Anne Mackay
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Michael A. Kouritzin: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton (Alberta), T6G 2G1, Canada
Anne Mackay: Department of Mathematics, Université du Québec à Montréal, Montréal (Québec), H3C 3P8, Canada

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 01, 1-29

Abstract: The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and volatility, especially for purposes of path-dependent option pricing. The resulting simulation algorithm is an analog to the weighted particle filtering algorithm that might be improved by resampling or branching. Indeed, some branching algorithms are shown herein to improve pricing performance substantially while some resampling algorithms are shown to be less suitable in certain cases. A historical property is given and explained as the distinguishing feature between the sequential Monte Carlo algorithms that work on path-dependent option pricing and those that do not. In particular, it is recommended to use the so-called effective particle branching algorithm within importance-sampling Monte Carlo methods for path-dependent option pricing. All recommendations are based upon numeric comparison of option pricing problems in the Heston model.

Keywords: American options; sequential Monte Carlo; branching processes; Heston model; stochastic approximation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S021902492050003X

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