A Study of Black-Scholes-Merton Model

Authors

  • Yichen Lin
  • Ruoyu Qian
  • Yihang Yan

DOI:

https://doi.org/10.61173/b0jadz18

Keywords:

Black-Scholes-Merton Model, Option Pricing Theory, Investment

Abstract

This study introduces the Option Pricing Theory improved by Black, Scholes, and Merton, which is also known as the Black-Scholes-Merton model, in detail and investigates its derivation process and historical development process. Despite the content above, it also includes its characteristics and mechanism. The newest Option Pricing formula proposed by Black, Scholes, and Merton was derived from mathematical methods such as the stochastic integral equation and Ito theorem. This essay concludes that the Black Scholes Merton model paved the way for the development and innovation of the subject of Financial Mathematics, which was found by the person who first came up with the Option Pricing Theory, which also contributes to the investment field to reduce the risk.

References

[1] Xu, C. Shiina, T (2018), Financial Investment, Financial Risk and Risk Management, Risk Management In Finance and Logistics[online]

[2] Nathalia, Astried Minang, Dalimunthe, Z (2019), Valuation of stock using the discounted cash flow model and Ministry of Finance regulation: Study of PT Indosat Tbk, Business Innovation and Development in Emerging Economies [online]

[3] Cotter, JF Peck, SW (2001), The structure of debt and active equity investors: The case of the buyout specialist, Journal of Financial Economics [online]

[4] Haven, E. (2005) Pilot-wave theory and financial option pricing, International Journal of Theoretical Physics [online].

[5] James E. Smith, Robert F. Nau (1995) Valuing Risky Projects - Option Pricing Theory and Decision-Analysis, Infrorms[online]

[6] Thomas J. O’Brien, Michael J. P. Selby (1986) Option Pricing Theory and Asset Expectations: A Review and Discussion in Tribute to James Boness, Wiley[online]

[7] Jovanovic, Franckm (2012) Bachelier: Not the forgotten forerunner he has been depicted as. An analysis of the dissemination of Louis Bachelier’s work in economics, European Journal of The History of Economic Thought[online]

[8] Edward J. Sullivan and Timothy M. Weithers (1991) Modern Option Pricing Theory - JSTOR, The Journal of Economic Education [online]

[9] BAFFES, J (1991) Some Further Evidence on the Law of One Price - The Law of One Price Still Holds, American Journal of Agricultural Economics[online]

[10] Elizondo, Rocio Padilla, P (2008) An analytical approach to Merton’s rational option pricing theory, Analysis and Applications [online]

[11] Shinde, S, A., Takale, C, K. (2012). Procedia Engineering, 38(2012)270-279

[12] Karatzas, I., & Shreve, S. E. (1998, January 1). Brownian Motion. Graduate Texts in Mathematics. 978-1-4612-0949-2

[13] Li, C., Liu, H., Liu, L., & Yao, Q. (2020, December 24). Pricing vulnerable options under jump diffusion processes using double Mellin transform. Communications in Statistics - Simulation and Computation, 52(3), 703–716.

[14] Jacod, J., & Protter, P. (2009, November 7). Risk-neutral compatibility with option prices. Finance and Stochastics, 14(2), 285–315.

[15] Gagnon, M. H., Power, G. J., & Toupin, D. (2014, August 15). Dynamics between crude oil and equity markets under the risk-neutral measure. Applied Economics Letters, 22(5), 370– 377.

[16] Dremkova, E., & Ehrhardt, M. (2011, September). A highorder compact method for nonlinear Black–Scholes option Dean&Francis pricing equations of American options. International Journal of Computer Mathematics, 88(13), 2782–2797.

[17] Ahir, H., Bloom, N., & Furceri, D. (2018). The world uncertainty index. https:// ssrn.com/abstract=3275033. Accessed on 22.09.2023.

[18] Zhuang, P., Liu, F., Anh, V., Turner, I. New solution and analytical techniques of the implicit numerical methods for the anomalous sub-diffusion equation, SIAM J. Numer. Anal. 46 (2) (2008) 1079–1095.

[19] Zhang, H., Liu, F., Turner, I., Yang, Q. (2016) Computers and Mathematics with Applications, 71(2016)1772-1783.

[20] Dar, A, A., Anutadha, N. (2017). Comparison: Binomial model and Black Scholes model, 1(2)230-245.

[21] Zhang, H., Liu, F., Turner, I., Chen, S. (2016). The numerical simulation of the tempered fractional Black-Scholes equation for European double barrier option, 40(2016)5819- 5834.

Downloads

Published

2024-08-14