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Asset Pricing with Second-Order Esscher Transforms

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  • Monfort, A.
  • Pegoraro, F.

Abstract

The purpose of the paper is to introduce, in a discrete-time no-arbitrage pricing context, a bridge between the historical and the risk-neutral state vector dynamics which is wider than the one implied by a classical exponential-affine stochastic discount factor (SDF) and to preserve, at the same time, the tractability and flexibility of the associated asset pricing model. This goal is achieved by introducing the notion of Exponential-Quadratic SDF or, equivalently, the notion of Second-Order Esscher Transform. The log-pricing kernel is specified as a quadratic function of the factor and the associated sources of risk are priced by means of possibly non-linear stochastic first-order and second-order risk-correction coefficients. Focusing on security market models, this approach is developed in the multivariate conditionally Gaussian framework and its usefulness is testified by the specification and calibration of what we name the Second-Order GARCH Option Pricing Model. The associated European Call option pricing formula generates a rich family of implied volatility smiles and skews able to match the typically observed ones.

Suggested Citation

  • Monfort, A. & Pegoraro, F., 2012. "Asset Pricing with Second-Order Esscher Transforms," Working papers 397, Banque de France.
    • Handle: RePEc:bfr:banfra:397
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    Cited by:

    1. Monfort, Alain & Pegoraro, Fulvio, 2012. "Asset pricing with Second-Order Esscher Transforms," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1678-1687.
    2. Antonio Diez de los Rios, 2017. "Optimal Estimation of Multi-Country Gaussian Dynamic Term Structure Models Using Linear Regressions," Staff Working Papers 17-33, Bank of Canada.
    3. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 457-493, June.
    4. Tong, Chen, 2024. "Pricing CBOE VIX in non-affine GARCH models with variance risk premium," Finance Research Letters, Elsevier, vol. 62(PA).
    5. Jean Barthélemy & Magali Marx, 2012. "Generalizing the Taylor Principle: New Comment," SciencePo Working papers hal-03461113, HAL.
    6. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    7. Markus Leippold & Nikola Vasiljević, 2020. "Option-Implied Intrahorizon Value at Risk," Management Science, INFORMS, vol. 66(1), pages 397-414, January.
    8. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.
    9. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2015. "Non-Gaussian GARCH option pricing models and their diffusion limits," European Journal of Operational Research, Elsevier, vol. 247(3), pages 820-830.
    10. repec:hal:spmain:info:hdl:2441/3bvs8clr5k9dqqcbq7j5ul2o65 is not listed on IDEAS
    11. repec:spo:wpmain:info:hdl:2441/3bvs8clr5k9dqqcbq7j5ul2o65 is not listed on IDEAS
    12. Bruno Feunou & Jean-Sébastien Fontaine, 2021. "Debt-Secular Economic Changes and Bond Yields," Staff Working Papers 21-14, Bank of Canada.
    13. Haruyoshi Ito & Jing Ai & Akihiko Ozawa, 2016. "Managing Weather Risks: The Case of J. League Soccer Teams in Japan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 877-912, December.
    14. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    15. Tahir Choulli & Ella Elazkany & Mich`ele Vanmaele, 2024. "The second-order Esscher martingale densities for continuous-time market models," Papers 2407.03960, arXiv.org.
    16. Jean Barthélemy & Magali Marx, 2012. "Generalizing the Taylor Principle: New Comment," Working Papers hal-03461113, HAL.
    17. Augustyniak, Maciej & Badescu, Alexandru & Bégin, Jean-François, 2023. "A discrete-time hedging framework with multiple factors and fat tails: On what matters," Journal of Econometrics, Elsevier, vol. 232(2), pages 416-444.
    18. 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.

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    More about this item

    Keywords

    Second-Order Esscher transform; exponential-quadratic stochastic discount factor; non-linear stochastic risk-correction coefficients; variance-covariance spread; Second-Order GARCH Option Pricing Model.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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