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مدل بلک شولز تعمیم یافته تحت نوسانات گارچ با محاسبه ارزش در معرض خطرشرطی در قیمت گذاری مشتقه | ||
راهبرد مدیریت مالی | ||
مقاله 3، دوره 11، شماره 4 - شماره پیاپی 43، دی 1402، صفحه 51-70 اصل مقاله (500.44 K) | ||
نوع مقاله: مقاله پژوهشی | ||
شناسه دیجیتال (DOI): 10.22051/jfm.2023.43857.2828 | ||
نویسندگان | ||
حسین نصرالهی1؛ محمدرضا حدادی* 2؛ منیژه گودرزی3 | ||
1گروه ریاضی مالی، دانشکده علوم پایه، دانشگاه آیت ا... بروجردی(ره)، بروجرد، ایران. | ||
2استادیار گروه ریاضی مالی، دانشکده علوم پایه، دانشگاه آیت ا... بروجردی(ره)، بروجرد، ایران. | ||
3گروه ریاضی، دانشکده علوم پایه، دانشگاه آیت ا... بروجردی (ره)، بروجرد، ایران. | ||
چکیده | ||
بازارهای مالی نقش اساسی در توسعه اقتصادی هر کشوری دارد، لذا بررسی دقیق این بازارها از جنبههای مختلف ضروری به نظر میرسد. حضور در این بازارها همواره با ریسک بالایی همراه است و به منظور کاهش ریسک ابزارهای مختلفی پدید آمده است. اختیار معامله، متداولترین ابزار معاملهای است که به بازارهای مالی معرفی شده است. مدل بلک شولز برای قیمتگذاری طیف وسیعی از قراردادهای اختیار معامله استفاده میشود. فرض اساسی در این مدل ثابت بودن نوسان بازدهها است که فرض مناسبی در دنیای واقعی نیست. هدف این پژوهش توسیع مدل بلک شولز تحت نوسانات تصادفی است. ابعاد نوآوری پژوهش شامل تحلیلی از عملکرد قیمتگذاری مدلها در طول دورههای کوتاهمدت، میانمدت و بلندمدت با ارزش در معرض خطر شرطی برای هر یک از قیمتها است. برای این منظور، از دادههای ایرانخودرو در بازه 1/9/ 1399 تا 23/9/ 1401 مورد استفاده قرار گرفت و نوسانات گارچ استاندارد و گارچ آستانه محاسبه و در مدل توسعهیافته بلک شولز بهکار گرفته شد. در ادامه قیمت اختیار خرید تحت مدل بلک شولز با نوسانات تاریخی، مدل بلک شولز توسعهیافته با گارچ استاندارد، گارچ آستانه و گارچ نمایی محاسبه شد. نتایج پژوهش حاکی از آن است که قیمت اختیار با نوسان تاریخی به قیمت واقعی بازار نزدیکتر است و همچنین، با توجه به ارزشدر معرض خطر شرطی بیشتر، ریسک واقعیتر نشان میدهد. در نهایت، برای آزمون نتایج بدست آمده قیمت اختیار خرید در هر چهار نوسان مفروض با روش مونت کارلو محاسبه و نتایج بدست آمده برای قیمتها تایید شد. | ||
کلیدواژهها | ||
نوسانات گارچ؛ قیمتگذاری اختیار؛ مدل بلکشولز؛ گارچ آستانه | ||
عنوان مقاله [English] | ||
Generalized Black-Scholes Model under Garch Volatility with Conditional value-at-risk Calculation in Derivative Pricing | ||
نویسندگان [English] | ||
Hossein Nasrollahi1؛ Mohammad Reza Haddadi2؛ Manizheh Goudarzi3 | ||
1Financial Mathematics Department, Ayatollah Borujerdi University, Borujerd, Iran. | ||
2Assistant Professor at Financial Mathematics, Faculty of Basic Sciences, Ayatollah Borujerdi University, Borujerd, Iran. | ||
3Department, of Mathematics and Statistics, Ayatollah Borujerdi University, Borujerd, Iran. | ||
چکیده [English] | ||
Financial markets play an essential role in the economic development of any country, therefore, a detailed examination of these markets from various aspects is necessary. Being in these markets is always associated with a high risk, and various tools have emerged in order to reduce the risk. Option is the most common trading tool that has been introduced to the financial markets. The Black-Scholes model is used to price a wide range of options contracts. The basic assumption in this model is the constant volatility of returns, which is not a suitable assumption in the real world. The aim of this research is to extend the Black-Scholes model under stachistic volatilities. The innovation of this research includes an analysis of the pricing performance of the models during the short, medium and long term periods with conditional value at risk for each of the prices. For this purpose, the data of Iran Khodro was used between 21/11/2020 to 14/12/2022 and the standard GARCH and threshold GARCH volatilities were calculated and used in the developed Black-Scholes model. In the following, the call option price was calculated under the Black-Scholes model with historical volatilities, the developed Black-Scholes model with standard GARCH, TGARCH and exponential GARCH. The results of the research indicate that the option price with historical volatility is closer to the real market price and also shows a more real risk due to the conditional value at risk. Finally, to test the obtained results, the price of the call option in all four assumed volatilities was calculated with Monte Carlo method and the obtained results were confirmed for the prices. | ||
کلیدواژهها [English] | ||
GARCH Volatility, Option Pricing, Black-Scholes Model, TGARCH | ||
سایر فایل های مرتبط با مقاله
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مراجع | ||
Abvali, M., Khalili Araghi, M., Hassanabadi, H., & Yaghoobnezhad, A., (2019). Optional Trading Pricing with a New Analytic Method for the Black-Scholes Equation. Journal of Financial Management Strategy, 7(26 ), 135-155. (in persian)
Amiri, M. (2020). Option Pricing Under Black– Scholes, Boness and Binomial Tree Models-Evidence from the Gold Coin Option Contracts in Iran Mercantile Exchange.Journal of Securities Exchange,13(50 ), 141-170. (in persian)
Angelidis, T., Benos, A., & Degiannakis, S. (2004). The use of GARCH models in VaR estimation. In Statistical Methodology (Vol. 1, Issues 1–2, pp. 105–128).
Baghestani, M., Pishbahar, E., & Dahsti, G. (2018). The Pricing of Asian Options Using Monte Carlo Simulation (Case Study: Soybean Meal). Agricultural Economics: Iranian Journal of Agricultural Economics (Economics and Agriculture Journal), 12(3 ), 1-26. (in persian)
Bahradmehr, N., & Tahmasebi, N. (2022). Pricing The Gold Coin Options of Iran Mercantile Exchange Market: "Black Scholes" and "Put-Call Parity" Approaches. Journal of Financial Economics (Financial Economics AND Development), 16(3 (60) ), 69-91. (in persian)
Black, F. (1976). Studies of stock market volatility changes. Proceedings of the American statistical association bisiness and economic statistics section,177-181.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. In Journal of Econometrics (Vol. 31, Issue 3, pp. 307–327).
Carr, P, & Wu, L. (2016). Analyzing volatility risk and risk premium in option contracts: A new theory. In Journal of Financial Economics (Vol. 120, Issue 1, pp.1–20).
Darabi, R., and Marufkhani, M. (2015). Valuation of new financial instruments. Auditor 18(82), 72-79. (in persian)
Duan, J. C. (1995). The GARCH option pricing model. Mathematical finance, 5(1), 13-32.
Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. In Econometrica (Vol. 50, Issue 4, p.987).
French , K. R., Schwert , G. W., & Staumbaugh, R. F. (1987). Expected Stock Returns and Volatility. Journal of Financial Economics(Vol. 19, Issue 1, pp.3-29).
Glosten, L. R, Jagannathan, R, & Runkle, D. E. (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. In The Journal of Finance (Vol. 48, Issue 5, pp. 1779–1801).
Gong, H, Thavaneswaran, A, & Singh, J. (2010). Stochastic Volatility Models with Application in Option Pricing. In Journal of Statistical Theory and Practice (Vol. 4, Issue 4, pp. 541–557).
Hajizadeh, E., & Mahootchi, M. (2019). A Simulation Based Optimization Model for Pricing Basket Options. Financial Engineering and Securities Management (Portfolio Management),10(38 ), 306-327. (in persian)
Harris ,D. (2018). Pricing European Style Options, University of rovidence, 1-49.
Hall, J. (2002). Fundamentals of financial engineering and risk management. Translated by Salehabadi, Ali, Sayah. Sajjad (2019). Tehran: Bors Information and Services Company, Bors Publications. (in persian).
İltüzer, Z. (2022). Option pricing with neural networks vs. Black-Scholes under different volatility forecasting approaches for BIST 30 index options. In Borsa Istanbul Review (Vol. 22, Issue 4, pp. 725–742).
Kimiagari, A. and Afride Sani, A. (2009), Presentation of an integrated method for option pricing based on two models, Black Shoeless and Binary Tree (Case Study of Iran Stock Exchange Market), International Quarterly Journal of Industrial Engineering and Production Management, 19(4), 119-127. (in persian)
Nissi, A, Maliki, B, and Rezaian, R. (2016). Estimating the parameters of the European option pricing model under the underlying asset with stochastic volatility using the loss function approach, Journal of Financial Engineering and Securities Management, 7(28), 91-115. (in persian)
Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. In Econometrica (Vol. 59, Issue 2, p. 347).
Pan, Z., Wang, Y., Liu, L., & Wang, Q. (2019). Improving volatility prediction and option valuation using VIX information: A volatility spillover GARCH model. In Journal of Futures Markets (Vol. 39, Issue 6, pp. 744–776).
Papantonis, I. (2016). Volatility risk premium implications of GARCH option pricing models. In Economic Modelling (Vol. 58, pp. 104–115).
Shahmoradi, A, & Zanganeh, M. (2016). Calculation of value at risk for major indices of Tehran Stock Exchange using parametric method. Journal of Economic Research, 42(79). 121-149. (in persian)
Sheraz, M., & Preda, V. (2014). Implied Volatility in Black-scholes Model with Garch Volatility. In Procedia Economics and Finance (Vol. 8, pp. 658–663).
Tehrani, R., Mohammadi, S., & Porebrahimi, M. (2011). Modeling and forecasting the volatility of Tehran Exchange Dividend Price Index (Tedpix). Financial Research Journal, 12(30), 23-36. (in persian)
Wang, X.-T., Zhao, Z.-F., & Fang, X.-F. (2015). Option pricing and portfolio hedging under the mixed hedging strategy. In Physica A: Statistical Mechanics and its Applications (Vol. 424, pp. 194–206).
Tsay, R. S. (2005). Analysis of financial time series. John wiley & sons.
Zakoian, J. M. (1994). Threshold heteroskedastic models. In Journal of Economic Dynamics and Control (Vol. 18, Issue 5, pp. 931–955).
Zhang, W., & Zhang, J. E. (2020). GARCH Option Pricing Models and the Variance Risk Premium. In Journal of Risk and Financial Management (Vol. 13, Issue 3, p. 51). | ||
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