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Asymptotic approach to the pricing of geometric asian options under the CEV model

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  • Lee, Min-Ku

Abstract

This paper studies the pricing of Asian options whose payoffs depend on the average value of an underlying asset during the period to a maturity. Since the Asian option is not so sensitive to the value of underlying asset, the possibility of manipulation is relatively small than the other options such as European vanilla and barrier options. We derive the pricing formula of geometric Asian options under the constant elasticity of variance (CEV) model that is one of local volatility models, and investigate the implication of the CEV model for geometric Asian options.

Suggested Citation

  • Lee, Min-Ku, 2016. "Asymptotic approach to the pricing of geometric asian options under the CEV model," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 544-548.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:544-548
    DOI: 10.1016/j.chaos.2016.07.013
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    References listed on IDEAS

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    1. Min-Ku Lee & Jeong-Hoon Kim & Kyu-Hwan Jang, 2014. "Pricing Arithmetic Asian Options under Hybrid Stochastic and Local Volatility," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, January.
    2. Ren Raw Chen & Cheng Few Lee & Han-Hsing Lee, 2020. "Empirical Performance of the Constant Elasticity Variance Option Pricing Model," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 51, pages 1903-1942, World Scientific Publishing Co. Pte. Ltd..
    3. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    4. John E. Angus, 1999. "A note on pricing Asian derivatives with continuous geometric averaging," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(7), pages 845-858, October.
    5. Jean-Pierre Fouque & George Papanicolaou & K. Ronnie Sircar, 2000. "Mean-Reverting Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 101-142.
    6. Hoi Ying Wong & Ying Lok Cheung, 2004. "Geometric Asian options: valuation and calibration with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 301-314.
    7. 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.
    8. Bin Peng, 2006. "Pricing Geometric Asian Options under the CEV Process," International Economic Journal, Taylor & Francis Journals, vol. 20(4), pages 515-522.
    9. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
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    Cited by:

    1. Yang, Xiangfeng & Zhang, Zhiqiang & Gao, Xin, 2019. "Asian-barrier option pricing formulas of uncertain financial market," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 79-86.
    2. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "Analytical valuation for geometric Asian options in illiquid markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 175-191.
    3. Zhang, Sumei & Gao, Xiong, 2019. "An asymptotic expansion method for geometric Asian options pricing under the double Heston model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 1-9.

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