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Two counters of jumps

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  • Câmara, António
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    Abstract

    This paper introduces a class of two counters of jumps option pricing models. The stock price follows a jump-diffusion process with price jumps up and price jumps down, where each type of jumps can have different means and standard deviations. Price jumps can be negatively autocorrelated as it has been observed in practice. We investigate the volatility surfaces generated by this class of two counters of jumps option pricing models. Our formulae, like the jump-diffusion models with a single counter of jumps, are able to generate smiles, and skews with similar shapes to those observed in the options markets. More importantly, unlike the jump-diffusion models with a single counter of jumps, our formulae are able to generate term structures of implied volatilities of at-the-money options with [intersection]-shaped patterns similar to those observed in the marketplace.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Banking & Finance.

    Volume (Year): 33 (2009)
    Issue (Month): 3 (March)
    Pages: 456-463

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    Handle: RePEc:eee:jbfina:v:33:y:2009:i:3:p:456-463

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    Web page: http://www.elsevier.com/locate/jbf

    Related research

    Keywords: Jump-diffusion Smile effect Term structure of implied volatilities;

    References

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    1. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "Pricing options on scenario trees," Journal of Banking & Finance, Elsevier, Elsevier, vol. 32(2), pages 283-298, February.
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    3. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, American Finance Association, vol. 52(5), pages 2003-49, December.
    4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 125-144.
    5. Amin, Kaushik I & Ng, Victor K, 1993. " Option Valuation with Systematic Stochastic Volatility," Journal of Finance, American Finance Association, American Finance Association, vol. 48(3), pages 881-910, July.
    6. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, American Finance Association, vol. 53(2), pages 499-547, 04.
    7. Chung, San-Lin & Wang, Yaw-Huei, 2008. "Bounds and prices of currency cross-rate options," Journal of Banking & Finance, Elsevier, Elsevier, vol. 32(5), pages 631-642, May.
    8. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 34(02), pages 211-239, June.
    9. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 58(3), pages 1269-1300, 06.
    10. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers, Yale School of Management ysm65, Yale School of Management.
    11. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers, University of California at Berkeley RPF-232, University of California at Berkeley.
    12. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, American Finance Association, vol. 49(3), pages 771-818, July.
    13. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers, Yale School of Management ysm54, Yale School of Management.
    14. Lioui, Abraham & Poncet, Patrice, 2005. "General equilibrium pricing of CPI derivatives," Journal of Banking & Finance, Elsevier, Elsevier, vol. 29(5), pages 1265-1294, May.
    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    16. Chang, Carolyn W. & S.K. Chang, Jack & Lim, Kian-Guan, 1998. "Information-time option pricing: theory and empirical evidence," Journal of Financial Economics, Elsevier, Elsevier, vol. 48(2), pages 211-242, May.
    17. Bakshi, Gurdip S & Chen, Zhiwu, 1997. " Equilibrium Valuation of Foreign Exchange Claims," Journal of Finance, American Finance Association, American Finance Association, vol. 52(2), pages 799-826, June.
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    Cited by:
    1. Koussis, Nicos & Martzoukos, Spiros H. & Trigeorgis, Lenos, 2013. "Multi-stage product development with exploration, value-enhancing, preemptive and innovation options," Journal of Banking & Finance, Elsevier, Elsevier, vol. 37(1), pages 174-190.
    2. Câmara, António & Krehbiel, Tim & Li, Weiping, 2011. "Expected returns, risk premia, and volatility surfaces implicit in option market prices," Journal of Banking & Finance, Elsevier, Elsevier, vol. 35(1), pages 215-230, January.
    3. Câmara, António & Popova, Ivilina & Simkins, Betty, 2012. "A comparative study of the probability of default for global financial firms," Journal of Banking & Finance, Elsevier, Elsevier, vol. 36(3), pages 717-732.
    4. Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, Elsevier, vol. 33(11), pages 2140-2149, November.

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