Automatic variance reduction for Monte Carlo simulations via the local importance function transform

The calculation of multivariate normal probabilities is of great importance in many statistical and economic applications. In this paper we propose a spherical Monte Carlo method with both theoretical analysis and numerical simulation. We start by writing the multivariate normal probability via an inner radial integral and an outer spherical integral using the spherical transformation. For the outer spherical integral, we apply an integration rule by randomly rotating a predetermined set of well-located points. To find the desired set, we derive an upper bound for the variance of the Monte Carlo estimator and propose a set which is related to the kissing number problem in sphere packings. For the inner radial integral, we employ the idea of antithetic variates and identify certain conditions so that variance reduction is guaranteed. Extensive Monte Carlo simulations on some probabilities confirm these claims.

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Monte Carlo Simulations for I-131 Imaging Using a Variance Reduction Technique

IFMBE Proceedings - World Congress on Medical Physics and Biomedical Engineering, September 7 - 12, 2009, Munich, Germany ◽

10.1007/978-3-642-03882-2_228 ◽

2009 ◽

pp. 856-858

Author(s):

H. R. Khosravi ◽

S. Sarkar ◽

H. Khosravi ◽

M. R. Deevband

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Variance Reduction ◽

Reduction Technique ◽

Variance Reduction Technique

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Efficient unbiased variance reduction techniques for Monte Carlo simulations of radiative transfer in cloudy atmospheres: The solution

Journal of Quantitative Spectroscopy and Radiative Transfer ◽

10.1016/j.jqsrt.2010.10.005 ◽

2011 ◽

Vol 112 (3) ◽

pp. 434-447 ◽

Cited By ~ 60

Author(s):

Robert Buras ◽

Bernhard Mayer

Keyword(s):

Monte Carlo ◽

Radiative Transfer ◽

Monte Carlo Simulations ◽

Variance Reduction ◽

Variance Reduction Techniques ◽

Reduction Techniques

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Option Pricing And Monte Carlo Simulations

Journal of Business & Economics Research (JBER) ◽

10.19030/jber.v3i9.2802 ◽

2011 ◽

Vol 3 (9) ◽

Author(s):

George M. Jabbour ◽

Yi-Kang Liu

Keyword(s):

Monte Carlo ◽

Option Pricing ◽

Monte Carlo Simulations ◽

Variance Reduction ◽

Closed Form Solution ◽

Form Solution ◽

Price Convergence ◽

Option Prices ◽

Black Scholes ◽

The Difference

The advantage of Monte Carlo simulations is attributed to the flexibility of their implementation. In spite of their prevalence in finance, we address their efficiency and accuracy in option pricing from the perspective of variance reduction and price convergence. We demonstrate that increasing the number of paths in simulations will increase computational efficiency. Moreover, using a t-test, we examine the significance of price convergence, measured as the difference between sample means of option prices. Overall, our illustrative results show that the Monte Carlo simulation prices are not statistically different from the Black-Scholes type closed-form solution prices.

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