Efficient quasi-Monte simulations for pricing high-dimensional path-dependent options |
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Authors: | Piergiacomo Sabino |
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Institution: | (1) Dipartimento di Matematica, Università degli Studi di Bari, Via Orabona 4, 70125 Bari, Italy |
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Abstract: | Quasi-Monte Carlo method (QMC) is an efficient technique for numerical integration. QMC provides a lower convergence rate,
O(ln
d
n/n), than the standard Monte Carlo (MC), , where n is the number of simulations and d the nominal problem dimension. However, some studies in the literature have claimed that the QMC performs better than the
MC method for d < 20/30 because of its dependence on d. Caflisch et al. (J Comput Finance 1(1):27–46, 1997) have proposed to extend the QMC superiority by ANOVA considerations.
To this aim, we consider the Asian basket option pricing problem, where d is much higher than 30, by QMC simulation. We investigate the applicability of several path-generation constructions that
have been proposed to overtake the dimensional drawback. We employ the principal component analysis, the linear transformation,
the Kronecker product approximation and test their performance both in terms of computational cost and accuracy. Finally,
we compare the results with those obtained by the standard MC.
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Keywords: | Monte Carlo Quasi-Monte Carlo Option pricing Path-generation techniques Path-dependent options |
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