Control Variates in Option Pricing

Authors

  • Tongyue Huang
  • Mingye Xiao
  • Ziyang Wang

DOI:

https://doi.org/10.61173/dwng4643

Keywords:

Monte Carlo simulation, Control variates, Option pricing

Abstract

This paper explores the application of Monte Carlo simulation in option pricing, comparing its advantages and limitations to help better understanding the complexities of financial derivatives. Then the paper further investigates the variance reduction strategy known as control variates, which can check how big the error appears in Monte Carlo simulation and improves the accuracy and efficiency of Monte Carlo simulations. This study presents a comprehensive analysis of theoretical foundations of control variates and Monte Carlo simulation, and use Python examples demonstrating the practical applications in financial market. The results highlight the value of sophisticated computational methods for enhancing the accuracy of option pricing and, eventually, facilitating better informed decision-making in a financial environment which is more and more complex now.

References

[1] Haug, E. G., & Taleb, N. N. (2011b). Option traders use (very) sophisticated heuristics, never the Black–Scholes–Merton formula. Journal of Economic Behavior & Organization, 77(2), 97–106. https://doi.org/10.1016/j.jebo.2010.09.013

[2] Andersen, L., & Broadie, M. (2004). Primal-Dual simulation algorithm for pricing multidimensional American options. Management Science, 50(9), 1222–1234. https://doi. org/10.1287/mnsc.1040.0258

[3] Glasserman, P. (2003). Monte Carlo methods in financial engineering. In Applications of mathematics. https://doi. org/10.1007/978-0-387-21617-1

[4] Boyle, P. P. (1977). Options: A Monte Carlo approach. Journal of Financial Economics, 4(3), 323–338. https://doi. org/10.1016/0304-405x(77)90005-8

[5] Heston, S. L. (1993). A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. Review of Financial Studies, 6(2), 327–343. https://doi.org/10.1093/rfs/6.2.327

[6] Fouque, J., Papanicolaou, G., & Sircar, K. R. (2000). Derivatives in Financial Markets with Stochastic Volatility. Cambridge University Press.

[7] Broadie, M., & Kaya, Ö. (2006). Exact simulation of stochastic volatility and other affine jump diffusion processes. Operations Research, 54(2), 217–231. https://doi.org/10.1287/ opre.1050.0247

[8] Broadie, M., & Glasserman, P. (1996). Estimating security price derivatives using simulation. Management Science, 42(2), 269–285. https://doi.org/10.1287/mnsc.42.2.269

[9] Giles, M. B. (2008). Multilevel Monte Carlo Path Simulation. Operations Research, 56(3), 607–617. https://doi.org/10.1287/ opre.1070.0496

Downloads

Published

2024-12-31

Issue

Vol. 2 No. 6 (2024): Volume 2, Issue 6

Section

Articles

License

Copyright (c) 2024 by the authors.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.