Sensitivity Estimation by Monte-Carlo Simulation Using Likelihood Ratio Method with Fixed-Sample-Path Principle

Koji Fukuda, Yasuyuki Kudo

2014

Abstract

The likelihood ratio method (LRM) is an efficient indirect method for estimating the sensitivity of given expectations with respect to parameters by Monte-Carlo simulation. The restriction on application of LRM to real-world problems is that it requires explicit knowledge of the probability density function (pdf) to calculate the score function. In this study, a fixed-sample-path method is proposed, which derives the score function required for LRM not via the pdf but directly from a constructive algorithm that computes the sample path from parameters and random numbers. The boundary residual, which represents the correction associated with the change of the distribution range of the random variables in LRM, is also derived. Some examples including the estimation of risk measures (Greeks) of option and financial flow-of-funds networks showed the effectiveness of the fixed-sample-path method.

References

  1. Bettonvil, B., 1989. 'A formal description of discrete event dynamic systems including infinitesimal perturbation analysis', European Journal of Operational Research, vol. 42, no. 2, pp. 213-222.
  2. Broadie, M., Glasserman P., 1996. 'Estimating security price derivatives using simulation', Management Science, vol. 42, no. 2, pp. 269-285.
  3. Ho, YC., Cao XR., 1991. Simulation and the Monte Carlo Method, Springer, 1991 edition.
  4. Glasserman, P., 2003. Monte Carlo Methods in Financial Engineering (Stochastic Modelling and Applied Probability), Springer, 2003 edition.
  5. Glynn, PW., 1987. 'Likelihood ratio gradient estimation: an overview', Proceedings of the 19th Winter Simulation Conference, pp. 366-374.
  6. Glynn, PW., 1989. 'Optimization of stochastic systems via simulation', Proceedings of the 21th Winter Simulation Conference, pp. 90-105.
  7. Rubinstein, RY., Kroese, DP., 2007. Simulation and the Monte Carlo Method, Wiley-Interscience, 2nd edition.
Download


Paper Citation


in Harvard Style

Fukuda K. and Kudo Y. (2014). Sensitivity Estimation by Monte-Carlo Simulation Using Likelihood Ratio Method with Fixed-Sample-Path Principle . In Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-038-3, pages 309-320. DOI: 10.5220/0005001603090320


in Bibtex Style

@conference{simultech14,
author={Koji Fukuda and Yasuyuki Kudo},
title={Sensitivity Estimation by Monte-Carlo Simulation Using Likelihood Ratio Method with Fixed-Sample-Path Principle},
booktitle={Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2014},
pages={309-320},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005001603090320},
isbn={978-989-758-038-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Sensitivity Estimation by Monte-Carlo Simulation Using Likelihood Ratio Method with Fixed-Sample-Path Principle
SN - 978-989-758-038-3
AU - Fukuda K.
AU - Kudo Y.
PY - 2014
SP - 309
EP - 320
DO - 10.5220/0005001603090320