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A semi-analytic pricing formula for lookback options under a general stochastic volatility model

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  • Park, Sang-Hyeon
  • Kim, Jeong-Hoon

Abstract

In general, the pricing problems of exotic options in finance do not have analytic solutions under stochastic volatility and so it is hard to compute the option prices or at least it requires much of time to compute them. This paper investigates a semi-analytic pricing method for lookback options in a general stochastic volatility framework. The resultant formula is well connected to the Black–Scholes price that is the first term of a series expansion, which makes computing the option prices relatively efficient. Further, a convergence condition for the expansion is provided with an error bound.

Suggested Citation

  • Park, Sang-Hyeon & Kim, Jeong-Hoon, 2013. "A semi-analytic pricing formula for lookback options under a general stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2537-2543.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:11:p:2537-2543
    DOI: 10.1016/j.spl.2013.08.002
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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, October.
    2. 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.
    3. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    4. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
    5. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    6. Roger W. Lee, 2001. "Implied And Local Volatilities Under Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 45-89.
    7. K. Ronnie Sircar & George Papanicolaou, 1999. "Stochastic volatility, smile & asymptotics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(2), pages 107-145.
    8. 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.
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    Cited by:

    1. Zhaoqiang Yang, 2017. "Efficient valuation and exercise boundary of American fractional lookback option in a mixed jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    2. Jiling Cao & Xi Li & Wenjun Zhang, 2023. "Pricing Path-Dependent Options under Stochastic Volatility via Mellin Transform," JRFM, MDPI, vol. 16(10), pages 1-17, October.
    3. Kim, Geonwoo & Jeon, Junkee, 2018. "Closed-form solutions for valuing partial lookback options with random initiation," Finance Research Letters, Elsevier, vol. 24(C), pages 321-327.
    4. Hu, Jun & Kanniainen, Juho, 2015. "Asymptotic expansion of European options with mean-reverting stochastic volatility dynamics," Finance Research Letters, Elsevier, vol. 14(C), pages 1-10.
    5. Jiling Cao & Jeong-Hoon Kim & Xi Li & Wenjun Zhang, 2022. "Pricing Path-dependent Options under Stochastic Volatility via Mellin Transform," Papers 2205.00573, arXiv.org.
    6. Kim, Jeong-Hoon & Park, Sang-Hyeon, 2014. "A recursive pricing formula for a path-dependent option under the constant elasticity of variance diffusion," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 39-47.
    7. Cao, Jiling & Kim, Jeong-Hoon & Li, Xi & Zhang, Wenjun, 2023. "Valuation of barrier and lookback options under hybrid CEV and stochastic volatility," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 660-676.

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