Pricing Options and Monte-Carlo Method a literature Review

Authors

  • Nier An
  • Bocheng Su

DOI:

https://doi.org/10.54691/bcpbm.v44i.4789

Keywords:

Monte Carlo Method; Option Pricing; Black-Scholes Model.

Abstract

This literature review provides an overview of the past and present of using Monte Carlo methods to price options. From the most B-S model to combining it with a Monte Carlo method, and then from a pricing model to a method for reducing the variance of the Monte Carlo method. Furthermore, building on the solid foundation of the previous research, more recent research has focused on integrating up to several hundred dimensions and even using machine learning methods to price options. This article aims to suggest a traceable path for beginners of Monte Carlo methods, providing them with a direction for learning.

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References

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F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Journal of political economy, vol. 81, no. 3, pp. 637–654, 1973.

R. C. Merton, “Theory of rational option pricing,” The Bell Journal of economics and management science, pp. 141–183, 1973.

P.P. Boyle, “Options: A monte Carlo approach,” Journal of financial economics, vol. 4, no. 3, pp. 323–338, 1977.

L. Rosenberg, “Bernstein polynomials and monte Carlo integration,” SIAM Journal on Numerical Analysis, vol. 4, no. 4, pp. 566–574, 1967.

S.L. Heston, “A closed-form solution for options with stochastic volatility with applications to bond and currency options,” The review of financial studies, vol. 6, no. 2, pp. 327–343, 1993.

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Y. Liang and X. Xu, “Variance and dimension reduction Monte Carlo method for pricing European multi-asset options with stochastic volatilities,” Sustainability, vol. 11, no. 3, p. 815, 2019.

V. Todorov, I. Dimov, and Y. Dimitrov, “Efficient quasi-monte Carlo methods for multiple integrals in option pricing,” in AIP Conference Proceedings, vol. 2025, p. 110007, AIP Publishing LLC, 2018.

L. Gan, H. Wang, and Z. Yang, “Machine learning solutions to challenges in finance: An application to the pricing of financial products,” Technological Forecasting and Social Change, vol. 153, p. 119928, 2020.

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Published

2023-04-27

How to Cite

An, N., & Su, B. (2023). Pricing Options and Monte-Carlo Method a literature Review. BCP Business & Management, 44, 29-35. https://doi.org/10.54691/bcpbm.v44i.4789