Quasi-Monte Carlo simulation of Brownian sheet with application to option pricing

Xinyu Song and Yazhen Wang

Statistical Theory and Related Fields, 2017, vol. 1, issue 1, 82-91

Abstract: Monte Carlo and quasi-Monte Carlo methods are widely used in scientific studies. As quasi-Monte Carlo simulations have advantage over ordinary Monte Carlo methods, this paper proposes a new quasi-Monte Carlo method to simulate Brownian sheet via its Karhunen–Loéve expansion. The proposed new approach allocates quasi-random sequences for the simulation of random components of the Karhunen–Loéve expansion by maximum reducing its variability. We apply the quasi-Monte Carlo approach to an option pricing problem for a class of interest rate models whose instantaneous forward rate driven by a different stochastic shock through Brownian sheet and we demonstrate the application with an empirical problem.

Date: 2017
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DOI: 10.1080/24754269.2017.1332965

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