COMPARISON OF THREE OPTION PRICING MODELS FOR INDIAN OPTIONS MARKET

Authors

DOI:

https://doi.org/10.29121/ijoest.v5.i4.2021.203

Keywords:

Black-Scholes Model, Modified Black­Scholes Model, Truncated Normal Distribution, Interest Rate, Options

Abstract

Black-Scholes option pricing model is used to decide theoretical price of different Options contracts in many stock markets in the world. In can find many generalizations of BS model by modifying some assumptions of classical BS model. In this paper we compared two such modified Black-Scholes models with classical Black-Scholes model only for Indian option contracts. We have selected stock options form 5 different sectors of Indian stock market. Then we have found call and put option prices for 22 stocks listed on National Stock Exchange by all three option pricing models. Finally, we have compared option prices for all three models and decided the best model for Indian Options. Motivation/Background: In 1973, two economists, Fischer Black, Myron and Robert Merton derived a closed form formula for finding value of financial options. For this discovery, they got a Nobel prize in Economic science in 1997. Afterwards, many researchers have found some limitations of Black-Scholes model. To overcome these limitations, there are many generalizations of Black-Scholes model available in literature. Also, there are very limited study available for comparison of generalized Black-Scholes models in context of Indian stock market. For these reasons we have done this study of comparison of two generalized BS models with classical BS model for Indian Stock market. Method: First, we have selected top 5 sectors of Indian stock market. Then from these sectors, we have picked total 22 stocks for which we want to compare three option pricing models. Then we have collected essential data like, current stock price, strike price, expiration time, rate of interest, etc. for computing the theoretical price of options by using three different option pricing formulas. After finding price of options by using all three models, finally we compared these theoretical option price with market price of respected stock options and decided that which theoretical price has less RMSE error among all three model prices. Result: After going through the method described above, we found that the generalized Black-Scholes model with modified distribution has minimum RMSE errors than other two models, one is classical Black-Scholes model and other is Generalized Black-Scholes model with modified interest rate.

Downloads

Download data is not yet available.

References

Black, F. & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy 81(3), 637–654. Retrieved from https://dx.doi.org/10.1086/260062 10.1086/260062

Dutta, K. K. & Babbel, D. F. (2005). Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions. The Journal of Business 78(3), 841–870. Retrieved from https://dx.doi.org/10.1086/429646 10.1086/429646

Fabozzi, F. J., Tunaru, R. & Albota, G. (2009). Estimating risk-neutral density with parametric models in interest rate markets. Quantitative Finance 9(1), 55–70. Retrieved from https://dx.doi.org/10.1080/14697680802272045 10.1080/14697680802272045

Godman, V. & Stampfli, J. The Mathematics Of Finance: Modelling And Hedging. .

Retrieved from Https://Www1.Nseindia.Com

Khan, M. U., Gupta, A. & Siraj, S. (2013). Empirical Testing Of Modified Black-Scholes Option Pricing Model Formula On NSE Derivative Market In India. International Journal Of Economics And Financial Issues 3(1), 87–98.

Khan, M. U., Gupta, A., Siraj, S. & Ravichandran, N. (2012). The Overview Of Financial Derivative And Its Products. International Journal Of Finance & Marketing 2(3), 57–72.

McDonald, J. B. & Bookstaber, R. M. (1991). Option pricing for generalized distributions. Communications in Statistics - Theory and Methods 20(12), 4053–4068. Retrieved from https://dx.doi.org/10.1080/03610929108830756 10.1080/03610929108830756

Peiro, A. (1999). Skewness In Financial Returns. J. Banking Finance 23(6), 847–862.

Rachev, S. T., Menn, C. & Fabozzi, F. J. (2005). Fat-Tailed And Skewed Asset Return Distributions: Implications For Risk Management, Portfolio Selection, And Option Pricing. John Wiley & Sons 139.

Savickas, R. (2002). A Simple Option-Pricing Formula. The Financial Review 37(2), 207–226. Retrieved from https://dx.doi.org/10.1111/1540-6288.00012 10.1111/1540-6288.00012

Sherrick, B. J., Garcia, P. & Tirupattur, V. (1996). Recovering probabilistic information from option markets: Tests of distributional assumptions. Journal of Futures Markets 16(5), 545–560. Retrieved from https://dx.doi.org/10.1002/(sici)1096-9934(199608)16:5<545::aid-fut3>3.0.co;2-g 10.1002/(sici)1096-9934(199608)16:5<545::aid-fut3>3.0.co;2-g

Zhu, S. P. & He, X. J. (2017). A Modified Black-Scholes Pricing Formula For European Options With Bounded Underlying Prices. Computers And Mathematics With Applications

Published

2021-07-20

How to Cite

Chauhan, A., & Gor, R. (2021). COMPARISON OF THREE OPTION PRICING MODELS FOR INDIAN OPTIONS MARKET. International Journal of Engineering Science Technologies, 5(4), 54–64. https://doi.org/10.29121/ijoest.v5.i4.2021.203

Most read articles by the same author(s)