Araştırma Makalesi
Option price computation under binary control regime switching triple-factor stochastic volatility model
Öz
This study presents an efficient pricing framework for European call options under a binary control regime that switches to a triple-factor stochastic volatility model, tailored for recessionary and stable market phases. The model captures regime transitions via binary controls and incorporates triple volatility sources. We derive the characteristic function and implement a semi-analytical pricing formula using trapezoidal and Gauss-Laguerre quadrature in MATLAB. The economic recovery process is influenced by the control parameter $\alpha$, while the impacts $\theta_3$ are considered secondary to other factors driving recovery. The results show that the option prices under recessionary conditions were lower compared to the recession-free regime, thereby validating the model{'}s sensitivity to macroeconomic uncertainty. It further confirms that the binary control regime switching triple-factor stochastic volatility model offers greater accuracy and adaptability across economic states, making it a promising tool for option pricing in dynamic financial environments.
Anahtar Kelimeler
Binary control economic recession option computation triple factor stochastic volatility.
Etik Beyan
The authors declare that there is no known ethical issue concerning this article.
Destekleyen Kurum
This research article did not benefit from any form of financial support.
Teşekkür
The authors appreciate the Department of Mathematics, University of Ibadan, for the thorough evaluation of the research content while undergoing this research.
Kaynakça
- [1] H. Albrecher, P.A. Mayer, W. Schoutens, and J. Tistaert, The Little Heston Trap, Wilmott Mag., 83–92, 2007.
- [2] P.A. Bankole, E.K. Ojo, and M.O. Odumosu, On recurrence relations and application in predicting price dynamics in the presence of economic recession, Int. J. Discrete Math. 2(4):125–131, 2017.
- [3] P.A. Bankole and O.O. Ugbebor, Fast Fourier transform based computation of American options under economic recession induced volatility uncertainty, J. Math. Finance 9:494–521, 2019.
- [4] P.A. Bankole and O.O. Ugbebor, Fast Fourier transform of multi-assets options under economic recession induced uncertainties, Am. J. Comput. Math. 9:143–157, 2019.
- [5] P.A. Bankole and I. Adinya, Options valuation with stochastic interest rate and recession-induced stochastic volatility, Trans. Niger. Assoc. Math. Phys. 16:291–304, 2021.
- [6] F. Black and M. Scholes, Valuation of options and corporate liabilities, J. Political Econ. 81:637–654, 1973.
- [7] P. Carr and D.B. Madan, Option valuation using fast Fourier transform, J. Comput. Finance 2(4):61–73, 1999.
- [8] N.B. Charlotte, J. Mung’atu, N.L. Abiodun, and M. Adjei, On modified Heston model for forecasting stock market prices, Int. J. Math. Trends Technol. 68(1):115–129, 2022.
- [9] P. Christoffersen, S. Heston, and J. Kris, The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well, Manag. Sci. 55:1914–1932, 2009.
- [10] D. Duffie, J. Pan, and K. Singleton, Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68:1343–1376, 2000.
- [11] S.E. Fadugba, A.M. Udoye, S.C. Zelibe, S.O. Edeki, C. Achudume, A.A. Adeyanju, O. Makinde, P.A. Bankole, and M.C. Kekana, Solving the Black-Scholes European options model using the reduced differential transform method with powered modified log-payoff function, Partial Differ. Equations Appl. Math. 13:101087, 2025.
- [12] J. Gao, R. Jia, I. Noorani, and F. Mehrdoust, Calibration of European option pricing model in uncertain environment: Valuation of uncertainty implied volatility, J. Comput. Appl. Math. 447:115890, 2024.
- [13] P. Gauthier and D. Possamaÿ, Efficient simulation of the double Heston model, Working Paper, Pricing Partners, 2010.
- [14] L.A. Grzelak, C.W. Oosterlee, and S. Van Weeren, Extension of stochastic volatility models with Hull-White interest rate process, Report 08-04, Delft Univ. Technol., 2008.
- [15] D. Guohe, Option pricing under two-factor stochastic volatility jump-diffusion model, Complexity, Article ID 1960121, 2020.
- [16] S.L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. Financ. Stud. 6(2):327–343, 1993.
- [17] S. Huang and G. Xunxiang, A Shannon wavelet method for pricing American options under two-factor stochastic volatilities and stochastic interest rate, Discrete Dyn. Nat. Soc., 2020.
- [18] H. Jiexiang, Z. Wenli, and R. Xinfeng, Option pricing using the fast Fourier transform under the double exponential jump model with stochastic volatility and stochastic intensity, J. Comput. Appl. Math. 263:152–159, 2014.
- [19] B. Liu, Uncertainty theory, 2nd ed., Springer-Verlag, Berlin, 2007.
- [20] B. Liu, Some research problems in uncertain theory, J. Uncertain Syst. 2(1):3–10, 2009.
- [21] Y. Liu and W. Lio, Power option pricing problem of uncertain exponential Ornstein- Uhlenbeck model, Chaos Solitons Fractals 178:114293, 2024.
- [22] V. Naik, Option valuation and hedging strategies with jumps in the volatility of asset returns, J. Finance 48:1969–1984, 1993.
- [23] P.A. Bankole, O.V. Olisama, E.K. Ojo, and I. Adinya, Fourier transform of stock asset returns uncertainty under Covid-19 surge, Filomat 38(8):2673–2690, 2024.
- [24] S.A. Raji, P.A. Bankole, and T.O. Olatunde, Mathematical model for Nigerian stock price returns under Covid-19 and economic insurgence induced volatility uncertainties, Quest J. Res. Appl. Math. 8(10):39–49, 2022.
- [25] F.D. Rouah, The Heston and Its Extensions in Matlab and C#, Wiley, Hoboken, 2013.
- [26] United Nations, World Economic Situation and Prospects 2025, Dep. Econ. Soc. Affairs, 1–190, 2024.
Yıl 2025,
Cilt: 54 Sayı: 3, 1049 - 1061, 24.06.2025
Öz
Kaynakça
- [1] H. Albrecher, P.A. Mayer, W. Schoutens, and J. Tistaert, The Little Heston Trap, Wilmott Mag., 83–92, 2007.
- [2] P.A. Bankole, E.K. Ojo, and M.O. Odumosu, On recurrence relations and application in predicting price dynamics in the presence of economic recession, Int. J. Discrete Math. 2(4):125–131, 2017.
- [3] P.A. Bankole and O.O. Ugbebor, Fast Fourier transform based computation of American options under economic recession induced volatility uncertainty, J. Math. Finance 9:494–521, 2019.
- [4] P.A. Bankole and O.O. Ugbebor, Fast Fourier transform of multi-assets options under economic recession induced uncertainties, Am. J. Comput. Math. 9:143–157, 2019.
- [5] P.A. Bankole and I. Adinya, Options valuation with stochastic interest rate and recession-induced stochastic volatility, Trans. Niger. Assoc. Math. Phys. 16:291–304, 2021.
- [6] F. Black and M. Scholes, Valuation of options and corporate liabilities, J. Political Econ. 81:637–654, 1973.
- [7] P. Carr and D.B. Madan, Option valuation using fast Fourier transform, J. Comput. Finance 2(4):61–73, 1999.
- [8] N.B. Charlotte, J. Mung’atu, N.L. Abiodun, and M. Adjei, On modified Heston model for forecasting stock market prices, Int. J. Math. Trends Technol. 68(1):115–129, 2022.
- [9] P. Christoffersen, S. Heston, and J. Kris, The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well, Manag. Sci. 55:1914–1932, 2009.
- [10] D. Duffie, J. Pan, and K. Singleton, Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68:1343–1376, 2000.
- [11] S.E. Fadugba, A.M. Udoye, S.C. Zelibe, S.O. Edeki, C. Achudume, A.A. Adeyanju, O. Makinde, P.A. Bankole, and M.C. Kekana, Solving the Black-Scholes European options model using the reduced differential transform method with powered modified log-payoff function, Partial Differ. Equations Appl. Math. 13:101087, 2025.
- [12] J. Gao, R. Jia, I. Noorani, and F. Mehrdoust, Calibration of European option pricing model in uncertain environment: Valuation of uncertainty implied volatility, J. Comput. Appl. Math. 447:115890, 2024.
- [13] P. Gauthier and D. Possamaÿ, Efficient simulation of the double Heston model, Working Paper, Pricing Partners, 2010.
- [14] L.A. Grzelak, C.W. Oosterlee, and S. Van Weeren, Extension of stochastic volatility models with Hull-White interest rate process, Report 08-04, Delft Univ. Technol., 2008.
- [15] D. Guohe, Option pricing under two-factor stochastic volatility jump-diffusion model, Complexity, Article ID 1960121, 2020.
- [16] S.L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. Financ. Stud. 6(2):327–343, 1993.
- [17] S. Huang and G. Xunxiang, A Shannon wavelet method for pricing American options under two-factor stochastic volatilities and stochastic interest rate, Discrete Dyn. Nat. Soc., 2020.
- [18] H. Jiexiang, Z. Wenli, and R. Xinfeng, Option pricing using the fast Fourier transform under the double exponential jump model with stochastic volatility and stochastic intensity, J. Comput. Appl. Math. 263:152–159, 2014.
- [19] B. Liu, Uncertainty theory, 2nd ed., Springer-Verlag, Berlin, 2007.
- [20] B. Liu, Some research problems in uncertain theory, J. Uncertain Syst. 2(1):3–10, 2009.
- [21] Y. Liu and W. Lio, Power option pricing problem of uncertain exponential Ornstein- Uhlenbeck model, Chaos Solitons Fractals 178:114293, 2024.
- [22] V. Naik, Option valuation and hedging strategies with jumps in the volatility of asset returns, J. Finance 48:1969–1984, 1993.
- [23] P.A. Bankole, O.V. Olisama, E.K. Ojo, and I. Adinya, Fourier transform of stock asset returns uncertainty under Covid-19 surge, Filomat 38(8):2673–2690, 2024.
- [24] S.A. Raji, P.A. Bankole, and T.O. Olatunde, Mathematical model for Nigerian stock price returns under Covid-19 and economic insurgence induced volatility uncertainties, Quest J. Res. Appl. Math. 8(10):39–49, 2022.
- [25] F.D. Rouah, The Heston and Its Extensions in Matlab and C#, Wiley, Hoboken, 2013.
- [26] United Nations, World Economic Situation and Prospects 2025, Dep. Econ. Soc. Affairs, 1–190, 2024.
Toplam 26 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Finansal Matematik |
| Bölüm | İstatistik |
| Yazarlar | |
| Erken Görünüm Tarihi | 1 Mayıs 2025 |
| Yayımlanma Tarihi | 24 Haziran 2025 |
| Gönderilme Tarihi | 25 Ağustos 2024 |
| Kabul Tarihi | 22 Nisan 2025 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 54 Sayı: 3 |