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Approximate option pricing and hedging in the CEV model via path-wise comparison of stochastic processes

Author

Listed:
  • Vladislav Krasin

    (Barclays Capital)

  • Ivan Smirnov

    (Susquehanna International Group)

  • Alexander Melnikov

    (University of Alberta)

Abstract

This paper presents a methodology of finding explicit boundaries for some financial quantities via comparison of stochastic processes. The path-wise comparison theorem is used to establish domination of the stock price process by a process with a known distribution that is relatively simple. We demonstrate how the comparison theorem can be applied in the constant elasticity of variance model to derive closed-form expressions for option price bounds, an approximate hedging strategy and a conditional value-at-risk estimate. We also provide numerical examples and compare precision of our method with the distribution-free approach.

Suggested Citation

  • Vladislav Krasin & Ivan Smirnov & Alexander Melnikov, 2018. "Approximate option pricing and hedging in the CEV model via path-wise comparison of stochastic processes," Annals of Finance, Springer, vol. 14(2), pages 195-209, May.
    • Handle: RePEc:kap:annfin:v:14:y:2018:i:2:d:10.1007_s10436-017-0309-9
    DOI: 10.1007/s10436-017-0309-9
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    References listed on IDEAS

    as
    1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    2. MacBeth, James D & Merville, Larry J, 1980. "Tests of the Black-Scholes and Cox Call Option Valuation Models," Journal of Finance, American Finance Association, vol. 35(2), pages 285-301, May.
    3. Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    4. Schepper, Ann De & Heijnen, Bart, 2007. "Distribution-free option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 179-199, March.
    5. Ding, Xiaodong & Wu, Rangquan, 1998. "A new proof for comparison theorems for stochastic differential inequalities with respect to semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 155-171, November.
    6. Jansen, K. & Haezendonck, J. & Goovaerts, M. J., 1986. "Upper bounds on stop-loss premiums in case of known moments up to the fourth order," Insurance: Mathematics and Economics, Elsevier, vol. 5(4), pages 315-334, October.
    7. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    8. 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.
    9. repec:bla:jfinan:v:44:y:1989:i:1:p:211-19 is not listed on IDEAS
    10. 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.
    11. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    More about this item

    Keywords

    Stochastic differential equations; Comparison theorem; Option pricing; Constant elasticity of variance model;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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