Stock Option Pricing by Augmented Monte-Carlo Simulation models

Document Type : Research Paper

Author

Department of Financial Management, Islamshahr Branch, Islamic Azad University, Islamshahr, Iran

10.22034/amfa.2019.1879290.1297

Abstract

Studying stock options is still a pristine area of research in the Iranian capital market. This is due to the lack of data as well as the complexity of valuation methodologies. In the present paper, using the Monte-Carlo simulation, we have estimated the value of stock options traded on Tehran Stock Exchange and examined whether the use of a control variate or antithetic variate augmented methods can lower the standard error of estimates. Furthermore, the estimated values of the three models under consideration, including crude Monte-Carlo, control variates augmented Monte-Carlo, and antithetic variates augmented Monte-Carlo are compared with each other and with options market prices. The results show that the standard error of the antithetic variate method is less than the crude method and control variate method. However, the control variate augmented Monte-Carlo model is more powerful than the crude Monte-Carlo and antithetic variate augmented Monte-Carlo method. Therefore, we can conclude that the control variate augmented Monte-Carlo model has a better performance in estimating the value of trading stock options and its estimated values are closer to the market prices.

Keywords


[1] Agarwal, A., Juneja, S., & Sircar, R., American options under stochastic volatility: control variates, maturity randomization & multiscale asymptotics, Quantitative Finance, 2016, 16(1), P. 17-30. Doi:10.1080/14697688.2015.1068443
 
[2] Alzubaidi, H., Efficient Monte Carlo Algorithm Using Antithetic Variate and Brownian Bridge Techniques for Pricing the Barrier Options with Rebate Payments, Journal of Mathematics and Statistics, 2016, 12, P. 1-11. Doi:10.3844/jmssp.2016.1.11
 
[3] Arnold, R. A., Microeconomics (9th Edition ed.). Cengage Learning, 2008.
 
[4] Ahmadi, R., Kordloei, H., The Effect of Financial Distress on the Investment Behavior of Companies Listed on Tehran Stock ExchangeAdvances in Mathematical Finance and Applications, 2018, 3(4), P. 17-28. Doi: 10.22034/amfa.2019.565459.1108
 
[5] Baird, A. J., Option Market Making: Trading and Risk Analysis for the Financial and Commodity Option Markets, John Wiley & Sons, 1992.
 
[5] Bayraktar, E., & Xing, H, Pricing Asian options for jump diffusion, Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics, 2011, 21(1), P. 117-143. Doi:10.1111/j.1467-9965.2010.00426.x
 
[6] Black, F., & Scholes, M., The pricing of options and corporate liabilities, Journal of political economy, 1973, 81(3), P. 637-654. Doi:10.1086/260062
 
[7] Bouaziz, L., Briys, E., & Crouhy, M., The pricing of forward-starting Asian options, Journal of Banking & Finance, 1994, 18(5), P. 823-839. Doi:10.1016/0378-4266(94)00031-X
 
[8] Boyle, P. P., Options: A monte carlo approach, Journal of financial economics, 1977, 4(3), P. 323-338. Doi:10.1016/0304-405X(77)90005-8
 
[9] Cox, J. C., & Ross, S. A., The valuation of options for alternative stochastic processes, Journal of financial economics, 1976, 3(1-2), P. 145-166. Doi:10.1016/0304-405X(76)90023-4
 
[10] Cox, J. C., Ross, S. A., & Rubinstein, M., Option pricing: A simplified approach, Journal of financial Economics, 1979, 7(3), P. 229-263. Doi:10.1016/0304-405X(79)90015-1
 
[11] Dibachi, H., Behzadi, M.H., Izadikhah, M., Stochastic multiplicative DEA model for measuring the efficiency and ranking of DMUs under VRS technology, Indian Journal of Science and Technology, 2014, 7 (11), P. 1765–1773. Doi: 10.17485/ijst/2014/v7i11.19
 
[12] Fu, M. C., & Hu, J.-Q., Sensitivity analysis for Monte Carlo simulation of option pricing, Probability in the Engineering and Informational Sciences, 1995, 9(3), P. 417-446. Doi:10.1017/S0269964800003958
 
[13] Grant, D., Vora, G., & Weeks, D., Path-dependent options: Extending the Monte Carlo simulation approach, Management Science, 1997, 43(11), P. 1589-1602. Doi:10.1287/mnsc.43.11.1589
 
[14] Healy, J., Variance Reduction of Ordinary MonteCarlo Estimates with the BrownianBridge Path Construction, Wilmott, 2018, 96, P. 54-57. Doi:10.1002/wilm.10693
 
[15] Izadikhah, M., Farzipoor Saen, R., Ranking sustainable suppliers by context-dependent data envelopment analysis. Ann Oper Res, 2020, 293, P.607–637, Doi: 10.1007/s10479-019-03370-4
 
[16] Izadikhah, M., Azadi, M., Shokri Kahi, V., Farzipoor Saen, R., Developing a new chance constrained NDEA model to measure the performance of humanitarian supply chains, International Journal of Production Research, 2019, 57(3), P. 662-682, Doi: 10.1080/00207543.2018.1480840
 
[17] Jackson, M., & Staunton, M., Advanced Modelling in Finance using Excel and VBA, John Wiley & Sons, 2006.
 
[18] Jeon, S., Hong, B., Kim, J., & Lee, H.-j., Stock Price Prediction based on Stock Big Data and Pattern Graph Analysis, IoTBD, 2016, P. 223-231. Doi:10.5220/0005876102230231
 
[19] Jia, J., Lai, Y., Li, L., & Tan, V., Exotic options pricing under special Lévy process models: a biased control variate method approach, Finance Research Letters, 2019, Doi:10.1016/j.frl.2019.07.022
 
[20] Lai, D. C., Tung, H. K., & Wong, M. C., Professional Financial Computing Using Excel and VBA, John Wiley & Sons, 2011.
 
[21] Lemieux, C., Control variates, Wiley StatsRef: Statistics Reference Online, 2017, P. 1-8. Doi:10.1002/9781118445112.stat07947
 
[21] Merton, R. C., Theory of Rational Option Pricing, The Bell Journal of Economics and Management Science, 1973, 4(1), P. 141-183. Doi:10.2307/3003143
 
[22] Mohebbi, M., & Gholizade Pasha, E., Stock Option Contracts Within Iran Legal Framework, Legal Researches, 2012, 63, P. 101-141. Doi:10.22034/rj.v16i63.1027, (in Persian)
 
[22] Nabavi Chashmi, S. A., & Ghasemi Chali, J., Appraisal Exotic Barrier Options in Tehran Stock Exchange, Journal of Investment Knowledge, 2017, 5(20), P. 205-222, (in Persian).
 
[22] Nakisa, R. C., A Financial Bestiary: Introducing Equity, Fixed Income, Credit, FX, Forwards, Futures, Options and Derivatives, Chesham Bois Publishing, 2010.
 
[23] Parsa, B., Sarraf, F., Financial Statement Comparability and the Expected Crash Risk of Stock PricesAdvances in Mathematical Finance and Applications, 2018, 3(3), P. 77-93. Doi: 10.22034/amfa.2018.544951
 
[23] Rafiei, M. T., & Absossamadi, R., Investigating the legal aspests of option contracts on stock exchanges, Private Law, 2006, 4(10), P. 77-114, (in Persian).
 
[24] Seifoddini, J., Roodposhti, F. R., & Nikoomaram, H., Parametric Estimates of High Frequency Market Microstructure Noise as an Unsystematic Risk, Jounral of money and Economy, 2015, 10(4), P. 29-50.
 
[25] Shabani, A., & Baharvandi, A., Futures and Options Contract at Jurisprudential Point of View, Islamic economics Studies, 2011, 3(5), P. 37-68, (in Persian).
 
[25] Salehi, A., Mohammadi, S., Afshari, M., Impact of Institutional Ownership and Board Independence on the Relationship Between Excess Free Cash Flow and Earnings ManagementAdvances in Mathematical Finance and Applications, 2017, 2(3), P. 91-105. Doi: 10.22034/amfa.2017.533104
 
[26] Vajargah, B. F., Salimipour, A., & Salahshour, S., Variance analysis of control variate technique and applications in Asian option pricing, International Journal of Industrial Mathematics, 2016, 8(1), P. 61-67.
 
[27] Wu, H., Pricing European options based on the fuzzy pattern of Black–Scholes formula, Computers & Operations Research, 2004, 31(7), P. 1069-1081. Doi:10.1016/S0305-0548(03)00065-0