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Option pricing in a conditional Bilateral Gamma model

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  • Fabio Bellini
  • Lorenzo Mercuri

Abstract

We propose a conditional Bilateral Gamma model, in which the shape parameters of the Bilateral Gamma distribution have a Garch-like dynamics. After risk neutralization by means of a Bilateral Esscher transform, the model admits a recursive procedure for the computation of the characteristic function of the underlying at maturity, à la Heston and Nandi (Rev Financ Stud 13(3):562–585, 2000 ). We compare the calibration performance on SPX options with the models of Heston and Nandi (Rev Financ Stud 13(3):562–585, 2000 ), Christoffersen et al. (J Econom 131(1–2):253–284, 2006 ) and with a dynamic variance Gamma model introduced in Mercuri and Bellini (J Financ Decis Mak 7(1):37–51, 2011 ), obtaining promising results. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Fabio Bellini & Lorenzo Mercuri, 2014. "Option pricing in a conditional Bilateral Gamma model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 373-390, June.
    • Handle: RePEc:spr:cejnor:v:22:y:2014:i:2:p:373-390
    DOI: 10.1007/s10100-013-0286-7
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    References listed on IDEAS

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    1. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    2. Shin Kim, Young & Rachev, Svetlozar T. & Leonardo Bianchi, Michele & Fabozzi, Frank J., 2010. "Tempered stable and tempered infinitely divisible GARCH models," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2096-2109, September.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    5. Mercuri, Lorenzo, 2008. "Option pricing in a Garch model with tempered stable innovations," Finance Research Letters, Elsevier, vol. 5(3), pages 172-182, September.
    6. Lorenzo Mercuri & Fabio Bellini, 2014. "Option Pricing in a Dynamic Variance-Gamma Model," Papers 1405.7342, arXiv.org.
    7. Christian Menn & Svetlozar Rachev, 2009. "Smoothly truncated stable distributions, GARCH-models, and option pricing," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 411-438, July.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    9. Monfort, Alain & Pegoraro, Fulvio, 2012. "Asset pricing with Second-Order Esscher Transforms," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1678-1687.
    10. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
    11. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
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    Cited by:

    1. Haibin Xie & Xinyu Wu & Pengying Fan, 2021. "Accelerating FHS Option Pricing Under Linear GARCH," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 395-411, August.
    2. Kazi Wahadul Hasan & Maliha Binte Hanif, 2022. "A pricing model for real-estate business in Bangladesh incorporating the uncertainty in buyer’s readiness: considerations during COVID-19 pandemic," SN Business & Economics, Springer, vol. 2(10), pages 1-16, October.
    3. Xie, Haibin & Wang, Shouyang & Lu, Zudi, 2018. "The behavioral implications of the bilateral gamma process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 259-264.
    4. Luiz Vitiello & Ivonia Rebelo, 2015. "A note on the pricing of multivariate contingent claims under a transformed-gamma distribution," Review of Derivatives Research, Springer, vol. 18(3), pages 291-300, October.

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