Nonparametric Estimation of Risk-Neutral Distribution via the Empirical Esscher Transform

This paper introduces an empirical version of the Esscher transform for nonparametric option pricing. Traditional parametric methods require the formulation of an explicit risk-neutral model and are operational only for a few probability distributions for the returns of the underlying asset. In our...

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Bibliographic Details
Published in:Revista Brasileira de Finanças 2017-06, Vol.15 (2), p.167-195
Main Authors: Pereira, Manoel, Veiga, Alvaro
Format: Article
Language:English
Subjects:
Arbitrage
Entropy
Equilibrium
Expected values
Methods
Nonparametric statistics
Prices
Probability
Probability distribution
Put & call options
Securities prices
Studies
Valuation
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Summary:This paper introduces an empirical version of the Esscher transform for nonparametric option pricing. Traditional parametric methods require the formulation of an explicit risk-neutral model and are operational only for a few probability distributions for the returns of the underlying asset. In our proposal, we make only mild assumptions on the pricing kernel and there is no need for the formulation of the risk-neutral model. First, we simulate sample paths for the returns under the physical measure. Then, based on the empirical Esscher transform, the sample is reweighted, giving rise to a risk-neutralized sample from which derivative prices can be obtained by a weighted sum of the options ' payoffs in each path. We analyze our proposal in experiments with artificial and real data.
ISSN:1679-0731
1984-5146