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Pricing Perpetual American Lookback Options Under Stochastic Volatility

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  • Min-Ku Lee

    (Kunsan National University)

Abstract

In this paper, we study the lookback option of the American style suggested in Dai (Journal of Computational Finance 4(2):63–68, 2000), and Dai and Kwok (SIAM Journal on Applied Mathematics 66(1):206–227, 2005) under stochastic volatility. By the asymptotic analysis introduced in Fouque et al. (Derivatives in financial markets with stochastic volatility, Cambridge University Press, Cambridge, 2000), we derive the explicit formula for the price and the optimal exercise value of the option with infinity maturity whose volatility follows the Ornstein–Uhlenbeck process. Especially, we investigate the effects of the stochastic volatility on the perpetual American lookback option in comparison with the constant volatility [cf. (Black and Scholes in The Journal of Political Economy 81(3):637–654, 1973] by using the results of the computational experiment.

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  • Min-Ku Lee, 2019. "Pricing Perpetual American Lookback Options Under Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1265-1277, March.
    • Handle: RePEc:kap:compec:v:53:y:2019:i:3:d:10.1007_s10614-017-9782-5
    DOI: 10.1007/s10614-017-9782-5
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584, July.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Ting, Sai Hung Marten & Ewald, Christian-Oliver & Wang, Wen-Kai, 2013. "On the investment–uncertainty relationship in a real option model with stochastic volatility," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 22-32.
    4. José Carlos Dias & João Pedro Vidal Nunes, 2011. "Pricing real options under the constant elasticity of variance diffusion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(3), pages 230-250, March.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. 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.
    7. Kim, Jeong-Hoon & Yoon, Ji-Hun & Lee, Jungwoo & Choi, Sun-Yong, 2015. "On the stochastic elasticity of variance diffusions," Economic Modelling, Elsevier, vol. 51(C), pages 263-268.
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    Cited by:

    1. Ha, Mijin & Kim, Donghyun & Yoon, Ji-Hun & Choi, Sun-Yong, 2025. "Pricing for perpetual American strangle options under stochastic volatility with fast mean reversion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 41-57.
    2. Xubiao He & Pu Gong, 2020. "A Radial Basis Function-Generated Finite Difference Method to Evaluate Real Estate Index Options," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 999-1019, March.

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