Document Type : Research Article
Author
Management and accounting, Allameh Tabataba'i university
Abstract
This study emphasizes on the mathematical modeling procedure of stock price behavior and option valuation in order to highlight the role and importance of advanced mathematics and subsequently computer software in financial analysis. To this end, following price process modeling and explaining the procedure of option pricing based on it, the resulting model is solved using advanced numerical methods and is executed by MATLAB software. As derivatives pricing models are based on price behavior of underling assets and are subject to change as a result of variation in the behavior of the asset, studying the price behavior of underlying asset is of significant importance. A number of such models (such as Geometric Brownian Motion and jump-diffusion model) are, therefore, analyzed in this article, and results of their execution based on real data from Tehran Stock Exchange total index are presented by parameter estimation and simulation methods and also by using numerical methods.
Keywords
[2] Andersen L. and J., Andreasen. (2000), Jump Diffusion Models: Volatility Smile Fitting and Numerical Methods for Pricing. Review of Derivatives Research ,4,231-262.
[3] Birkohff, Garrett. (1998), Ordinary Differential Equations, New York.
[4] Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.
[5] Brownlees, C. T., Gallo, G. M. (2010). Comparison of volatility measures: a risk management perspective. Journal of Financial Econometrics, 8(1), 29-56.
[7] Hull, John C. (2018), Fundamentals of Futures and Options Markets and Derivatives Package, 10th Edition, Prentice Hall.
[8] Jin-Chuan Duan, Ivilina Popova and Peter Ritchken. (2002), Option Pricing Under Regime Switching,Quantitative Finance,2, pp. 1-17.
[9] Karimnejad Esfahani, M., Neisy, A., De Marchi, S. (2020). An RBF approach for oil futures pricing under the jump-diffusion model. Journal of Mathematical Modeling, 1-12.
[10] Klugman S. A., H. H. Panjer, G. E. Willmot. (2005), Loss Model from Data to Decisions, Wiley, USA.
[11] Kou S. G. and Hui Wang. (2003), First Passage Times of a Jump Diffusion Process. Adv. Appl. Prob., Vol 35, pp. 504.
[12] Kou S. G., A (2002). Jump-Diffusion Model for Option Pricing. Management Science, 48, No. 8, pp. 1086-1101.
[13] Laura-Diana Radu. (2009). Qualitative, Semi-Quantitative and, Quantitative Methods for Risk Assessment: Case Of The Financial Audit, Analele Stiinti ceale Universitatii "Alexandru Ioan Cuza" din Iasi - Stiinte Economice, Alexandru
Ioan Cuza University, Faculty of Economics and Business Administration, vol. 56, pages 643-657, November.
[14] Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of economics and management science, 141-183.
[15] Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of nancial economics, 3(1-2), 125-144.
[16] Mohamadinejad, Reyhane Biazar, Jafar Neisy, Abdolsadeh. (2020). Spread Option Pricing Using Two Jump-Diffusion Interest Rates. UPB Scienti c Bulletin, Series A: Applied Mathematics and Physics. 28.
[17] Oksendal, Bernt. (1998), Stochastic Differential Equations, Springer-Verlag Berlin Heidelberg.
[18] Peymany, M., Hooshangi, Z. (2017). Estimation and Comparison of Short-TermInterest Rate Equilibrium Models Using Islamic Treasury Bills. Financial Engineering and Portfolio Management, 8(33), 89-111.Wilmott, Paul. (2006), Paul Wilmotton quantitative nance, Wiley Sons.
)