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Valuation of Standard Options under the Constant Elasticity of Variance Model

Author

Listed:
  • Richard Lu

    (Department of Insurance, Feng Chia University, Taiwan)

  • Yi-Hwa Hsu

    (Merry Electronics Co., Ltd., Taiwan)

Abstract

A binomial model is developed to value options when the underlying process follows the constant elasticity of variance (CEV) model. This model is proposed by Cox and Ross (1976) as an alternative to the Black and Scholes (1973) model. In the CEV model, the stock price change (dS) has volatility £mS £]/2 instead of £mS in the Black-Scholes model. The rationale behind the CEV model is that the model can explain the empirical bias exhibited by the Black-Scholes model, such as the volatility smile. The option pricing formula when the underlying process follows the CEV model is derived by Cox and Ross (1976), and the formula is further simplified by Schroder (1989). However, the closed-form formula is useful in some limited cases. In this paper, a binomial process for the CEV model is constructed to yield a simple and efficient computation procedure for practical valuation of standard options. The binomial option pricing model can be employed under general conditions. Also, on average, the numerical results show the binomial option pricing model approximates better than other analytic approximations.

Suggested Citation

  • Richard Lu & Yi-Hwa Hsu, 2005. "Valuation of Standard Options under the Constant Elasticity of Variance Model," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 4(2), pages 157-165, August.
    • Handle: RePEc:ijb:journl:v:4:y:2005:i:2:p:157-165
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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. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(4), pages 533-554, November.
    4. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    5. Beckers, Stan, 1980. "The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-673, June.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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    Cited by:

    1. Hi Jun Choe & Jeong Ho Chu & So Jeong Shin, 2014. "Recombining binomial tree for constant elasticity of variance process," Papers 1410.5955, arXiv.org.
    2. Axel A. Araneda & Marcelo J. Villena, 2018. "Computing the CEV option pricing formula using the semiclassical approximation of path integral," Papers 1803.10376, arXiv.org.
    3. U Hou Lok & Yuh-Dauh Lyuu, 2022. "A Valid and Efficient Trinomial Tree for General Local-Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 817-832, October.
    4. U Hou Lok & Yuh‐Dauh Lyuu, 2020. "Efficient trinomial trees for local‐volatility models in pricing double‐barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(4), pages 556-574, April.

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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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