Comparison of Selected Methods for Option Pricing Using C++

Lun Gao

Master's thesis

Abstract:

Since the Black-Scholes model was born in the 1970s, option pricing has always been an important research object in the mathematical and financial community. Its related research on option pricing has extensive and far-reaching effects on the entire capital market. However, general Black-Scholes partial differential equations cannot solve American options that can be exercised in advance. Therefore, more and more researchers use the least squares Monte Carlo simulation, binomial tree method and finite difference method to calculate the option price. This paper studies the pricing of options using Black-Scholes, Monte Carlo simulation，least square Monte Carlo simulation, binomial tree method, and finite difference method through the risk-neutral measure of backward stochastic differential equations. Through these methods, the numerical simulation of option pricing under backward stochastic differential equations is given, and some valuable results are obtained. In this paper, the meaning of the model parameters is explained before the empirical research is pushed to the Black-Scholes formula. After downloading some data from the Hong Kong Stock Exchange and the Chicago Futures Exchange, various methods were used to conduct price simulations to obtain the option values under different parameters. The results show that the option prices calculated in the complete market are slightly different from those in the incomplete market but apparently tend to be consistent and have a good degree of fit. At the end of the article, the difference between theoretical value and market value is explained.

Abstract:

Since the Black-Scholes model was born in the 1970s, option pricing has always been an important research object in the mathematical and financial community. Its related research on option pricing has extensive and far-reaching effects on the entire capital market. However, general Black-Scholes partial differential equations cannot solve American options that can be exercised in advance. Therefore, more and more researchers use the least squares Monte Carlo simulation, binomial tree method and finite difference method to calculate the option price. This paper studies the pricing of options using Black-Scholes, Monte Carlo simulation，least square Monte Carlo simulation, binomial tree method, and finite difference method through the risk-neutral measure of backward stochastic differential equations. Through these methods, the numerical simulation of option pricing under backward stochastic differential equations is given, and some valuable results are obtained. In this paper, the meaning of the model parameters is explained before the empirical research is pushed to the Black-Scholes formula. After downloading some data from the Hong Kong Stock Exchange and the Chicago Futures Exchange, various methods were used to conduct price simulations to obtain the option values under different parameters. The results show that the option prices calculated in the complete market are slightly different from those in the incomplete market but apparently tend to be consistent and have a good degree of fit. At the end of the article, the difference between theoretical value and market value is explained.

Keywords

Option pricing, Taylor's Formula, Wiener process, Black-Scholes model, Gaussian distribution, Monte Carlo simulation, least square Monte Carlo simulation, Finite difference method, Binomial tree method, C++

Keywords

Option pricing, Taylor's Formula, Wiener process, Black-Scholes model, Gaussian distribution, Monte Carlo simulation, least square Monte Carlo simulation, Finite difference method, Binomial tree method, C++

Language used: English

Date on which the thesis was submitted / produced: 27. 4. 2018

Thesis defence

• Date of defence: 28. 5. 2018
• Supervisor: Tomáš Tichý
• Reader: Miroslav Čulík

VŠB - Technical University of Ostrava

Ekonomická fakulta

Master programme / field:
Hospodářská politika a správa / Finance