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Asset Pricing with Second-Order Esscher Transforms

Author

Listed:
  • Alain MONFORT

    (Crest)

  • Fulvio PEGORARO

    (Crest)

Abstract
The purpose of the paper is to introduce, in the class of discrete time no-arbitrage asset pricing models, awider bridge between the historical and the risk-neutral state vector dynamics and to preserve, at the same time,its tractability and °exibility. This goal is achieved by introducing the notion of Exponential-Quadratic stochasticdiscount factor (SDF) or, equivalently, the notion of Second-Order Esscher Transform. Then, focusing on securitymarket models, this approach is developed in three important multivariate stochastic frameworks: the conditionallyGaussian framework, the conditionally Mixed-Normal and the conditionally Gaussian Switching Regimes framework.In the conditionally multivariate Gaussian case, our approach determines a risk-neutral mean as a function of(the short rate and of) the risk-neutral variance-covariance matrix which is di®erent from the historical one. Theconditionally mixed-normal Gaussian case provides a ¯rst generalization of the Gaussian setting, in which the risk-neutral variance-covariance matrices and mixing weights of all components (in the ¯nite mixture) can be di®erentfrom the historical ones. The Gaussian switching regime case introduces further °exibility given the serial dependenceof regimes and the introduction of the regime indicator function in the exponential-quadratic SDF. We also developswitching regime models which include (in the factor's conditional mean and conditional variance) additive impactsof the present and past regimes and we stress their interpretation in terms of general "discrete-time jump-di®usion"models in which the risk included in the ¯rst and second moment of jumps is priced.Even if we focus on security market models, we do not make any particular assumption about the state vectorand therefore this appr

Suggested Citation

  • Alain MONFORT & Fulvio PEGORARO, 2010. "Asset Pricing with Second-Order Esscher Transforms," Working Papers 2010-54, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2010-54
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    References listed on IDEAS

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    2. 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.
    3. Jean Barthélemy & Magali Marx, 2012. "Generalizing the Taylor Principle: New Comment," SciencePo Working papers hal-03461113, HAL.
    4. Markus Leippold & Nikola Vasiljević, 2020. "Option-Implied Intrahorizon Value at Risk," Management Science, INFORMS, vol. 66(1), pages 397-414, January.
    5. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    6. repec:hal:spmain:info:hdl:2441/3bvs8clr5k9dqqcbq7j5ul2o65 is not listed on IDEAS
    7. 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.
    8. Jean Barthélemy & Magali Marx, 2012. "Generalizing the Taylor Principle: New Comment," SciencePo Working papers Main hal-03461113, HAL.
    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. Tahir Choulli & Ella Elazkany & Mich`ele Vanmaele, 2024. "The second-order Esscher martingale densities for continuous-time market models," Papers 2407.03960, arXiv.org.
    11. Tong, Chen, 2024. "Pricing CBOE VIX in non-affine GARCH models with variance risk premium," Finance Research Letters, Elsevier, vol. 62(PA).
    12. Tahir Choulli & Ella Elazkany & Mich`ele Vanmaele, 2024. "Applications of the Second-Order Esscher Pricing in Risk Management," Papers 2410.21649, arXiv.org.
    13. 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.
    14. 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.
    15. Bruno Feunou & Jean-Sébastien Fontaine, 2021. "Debt-Secular Economic Changes and Bond Yields," Staff Working Papers 21-14, Bank of Canada.
    16. 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.
    17. 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.
    18. 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.
    19. 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.

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    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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