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Pricing European option with the short rate under Subdiffusive fractional Brownian motion regime

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  • Foad Shokrollahi

Abstract

The purpose of this paper is to analyze the problem of option pricing when the short rate follows subdiffusive fractional Merton model. We incorporate the stochastic nature of the short rate in our option valuation model and derive explicit formula for call and put option and discuss the corresponding fractional Black-Scholes equation. We present some properties of this pricing model for the cases of $\alpha$ and $H$. Moreover, the numerical simulations illustrate that our model is flexible and easy to implement.

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  • Foad Shokrollahi, 2018. "Pricing European option with the short rate under Subdiffusive fractional Brownian motion regime," Papers 1805.00792, arXiv.org.
    • Handle: RePEc:arx:papers:1805.00792
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    References listed on IDEAS

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    1. Sottinen Tommi & Valkeila Esko, 2003. "On arbitrage and replication in the fractional Black–Scholes pricing model," Statistics & Risk Modeling, De Gruyter, vol. 21(2), pages 93-108, February.
    2. Cipian Necula, 2008. "Option Pricing in a Fractional Brownian Motion Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 2, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    3. Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012. "Time-changed geometric fractional Brownian motion and option pricing with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3971-3977.
    4. Wang, Jun & Liang, Jin-Rong & Lv, Long-Jin & Qiu, Wei-Yuan & Ren, Fu-Yao, 2012. "Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 750-759.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Kung, James J. & Lee, Lung-Sheng, 2009. "Option pricing under the Merton model of the short rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 378-386.
    7. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
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