Nonparametric Option Pricing with Generalized Entropic Estimators

35 Pages Posted: 10 Dec 2014 Last revised: 2 May 2022

See all articles by Caio Almeida

Caio Almeida

Princeton University

Gustavo Freire

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE); Tinbergen Institute; Erasmus Research Institute of Management (ERIM)

Rafael Azevedo

Getulio Vargas Foundation (FGV)

Kym Ardison

Getulio Vargas Foundation (FGV) - FGV/EPGE Escola Brasileira de Economia e Finanças

Date Written: April 29, 2022

Abstract

We propose a family of nonparametric estimators for an option price that require only the use of underlying return data, but can also easily incorporate information from observed option prices. Each estimator comes from a risk-neutral measure minimizing generalized entropy according to a different Cressie-Read discrepancy. We apply our method to price S&P 500 options and the cross-section of individual equity options, using distinct amounts of option data in the estimation. Estimators incorporating mild nonlinearities produce optimal pricing accuracy within the Cressie-Read family and outperform several benchmarks such as the Black-Scholes and different GARCH option pricing models. Overall, we provide a powerful option pricing technique suitable for scenarios of limited option data availability.

Keywords: Risk-Neutral Measure, Option Pricing, Risk Premium, Nonparametric Estimation, Stochastic Volatility, Jumps, Cressie-Read Discrepancies

JEL Classification: C1, C5, C6, G1

Suggested Citation

Almeida, Caio and Freire, Gustavo and Azevedo, Rafael and Ardison, Kym, Nonparametric Option Pricing with Generalized Entropic Estimators (April 29, 2022). Available at SSRN: https://ssrn.com/abstract=2535790 or http://dx.doi.org/10.2139/ssrn.2535790

Caio Almeida (Contact Author)

Princeton University ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States

Gustavo Freire

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands

HOME PAGE: http://https://www.eur.nl/people/gustavo-freire

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

HOME PAGE: http://https://tinbergen.nl/person/2029/gustavo-freire

Erasmus Research Institute of Management (ERIM) ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

HOME PAGE: http://https://www.erim.eur.nl/people/gustavo-freire/

Rafael Azevedo

Getulio Vargas Foundation (FGV) ( email )

R. Dr. Neto de Araujo 320 cj 1307
Rio de Janeiro, Rio de Janeiro 22250-900
Brazil

Kym Ardison

Getulio Vargas Foundation (FGV) - FGV/EPGE Escola Brasileira de Economia e Finanças ( email )

Praia de Botafogo 190/1125, CEP
Rio de Janeiro RJ 22253-900
Brazil

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