Asset pricing with Second-Order Esscher Transforms

► The main idea is to enlarge the standard bridge between the historical and the risk neutral worlds, by introducing the notions of Second Order Laplace Transform, Second Order Esscher Transform and exponential quadratic stochastic discount factor. ► An application to option pricing is provided. The...

Full description

Saved in:
Bibliographic Details
Published in:Journal of banking & finance 2012-06, Vol.36 (6), p.1678-1687
Main Authors: Monfort, Alain, Pegoraro, Fulvio
Format: Article
Language:English
Subjects:
Asset pricing
Exponential-quadratic stochastic discount factor
GARCH models
Non-linear stochastic risk-correction coefficients
Probability distribution
Put & call options
Risk management
Second-Order Esscher Transform
Second-Order GARCH Option Pricing Model
Securities issues
Securities prices
Stochastic models
Stochastic processes
Studies
Volatility
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:► The main idea is to enlarge the standard bridge between the historical and the risk neutral worlds, by introducing the notions of Second Order Laplace Transform, Second Order Esscher Transform and exponential quadratic stochastic discount factor. ► An application to option pricing is provided. 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.
ISSN:0378-4266
1872-6372
DOI:10.1016/j.jbankfin.2012.01.014