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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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    Citations

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    Cited by:

    1. Barthélemy, J. & Marx, M., 2012. "Generalizing the Taylor Principle: New Comment," Working papers 403, Banque de France.
    2. Monfort, Alain & Pegoraro, Fulvio, 2012. "Asset pricing with Second-Order Esscher Transforms," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1678-1687.
    3. repec:bla:jrinsu:v:83:y:2016:i:4:p:877-912 is not listed on IDEAS
    4. 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.
    5. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 457-493, June.
    6. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

    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.;

    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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