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

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.

KEYWORDS:

• Brownian sheet
• Karhunen–Loéve expansion
• Monte Carlo
• option pricing
• Quasi-Monte Carlo

Acknowledgements

The research of Yazhen Wang was supported in part by NSF [grant number DMS-12-65203], [grant number DMS-15-28375].

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Yazhen Wang was supported in part by NSF [grant number DMS-12-65203], [grant number DMS-15-28375]

Notes on contributors

Xinyu Song

Xinyu Song is a graduate student in the Department of Statistics at University of Wisconsin-Madison. Her research interests are in modelling financial instruments, particularly based on high frequency data.

Yazhen Wang

Yazhen Wang is professor of statistics at the University of Wisconsin-Madison and also serves as Chair for the Department of Statistics at University of Wisconsin-Madison. His major research interests are in financial statistics and financial data science (both high frequency and low frequency), quantum computing as well as high dimensional statistics and statistics learning. He holds fellowship at Institute of Mathematical Statistics (IMS) and at American Statistical Association (ASA).