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A recursive pricing formula for a path-dependent option under the constant elasticity of variance diffusion

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

Abstract

In this paper, we consider a path-dependent option in finance under the constant elasticity of variance diffusion. We use a perturbation argument and the probabilistic representation (the Feynman–Kac theorem) of a partial differential equation to obtain a complete asymptotic expansion of the option price in a recursive manner based on the Black–Scholes formula and prove rigorously the existence of the expansion with a convergence error.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:94:y:2014:i:c:p:39-47
    DOI: 10.1016/j.spl.2014.07.004
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    References listed on IDEAS

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    1. repec:bla:jfinan:v:44:y:1989:i:1:p:211-19 is not listed on IDEAS
    2. 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.
    3. 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.
    4. 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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