Asset Pricing with Second-Order Esscher Transforms

Alain Monfort and Fulvio Pegoraro ()

Working papers from Banque de France

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.

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. (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2012
New Economics Papers: this item is included in nep-ore
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Citations: View citations in EconPapers (14)

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Related works:
Journal Article: Asset pricing with Second-Order Esscher Transforms (2012)
Working Paper: Asset Pricing with Second-Order Esscher Transforms (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:bfr:banfra:397

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