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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.

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Bibliographic Info

Paper provided by Banque de France in its series Working papers with number 397.

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Length: 36 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:bfr:banfra:397

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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.;

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Citations

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Cited by:
  1. Monfort, A. & Pegoraro, F., 2012. "Asset Pricing with Second-Order Esscher Transforms," Working papers 397, Banque de France.
  2. Matthias Fengler & Helmut Herwartz & Christian Werner, 2010. "A dynamic copula approach to recovering the index implied volatility skew," University of St. Gallen Department of Economics working paper series 2010 1132, Department of Economics, University of St. Gallen, revised Nov 2011.
  3. 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.
  4. 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.

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