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Option pricing with maximum entropy densities: The inclusion of higher‐order moments

Option pricing with maximum entropy densities: The inclusion of higher‐order moments Entropy pricing applies notions of information theory to derive the theoretical value of options. This paper employs the maximum entropy (ME) formulation of option pricing, given risk‐neutral moment constraints computed directly from the observed prices. First, higher‐order moments are used to generate option prices. Then a generalization of Shannon entropy, known as Renyi entropy, is studied to account for extreme events. This ME problem provides a class of heavy‐tailed distributions. Examples and Monte Carlo simulations are provided to examine the effects of moment constraints on option prices. The call option values are then constructed using daily Standard and Poor's 500 index options. The findings suggest that entropy pricing with higher‐order moment constraints provides higher forecasting accuracy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Futures Markets Wiley

Option pricing with maximum entropy densities: The inclusion of higher‐order moments

The Journal of Futures Markets , Volume 42 (10) – Oct 1, 2022

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References (61)

Publisher
Wiley
Copyright
© 2022 Wiley Periodicals LLC.
ISSN
0270-7314
eISSN
1096-9934
DOI
10.1002/fut.22361
Publisher site
See Article on Publisher Site

Abstract

Entropy pricing applies notions of information theory to derive the theoretical value of options. This paper employs the maximum entropy (ME) formulation of option pricing, given risk‐neutral moment constraints computed directly from the observed prices. First, higher‐order moments are used to generate option prices. Then a generalization of Shannon entropy, known as Renyi entropy, is studied to account for extreme events. This ME problem provides a class of heavy‐tailed distributions. Examples and Monte Carlo simulations are provided to examine the effects of moment constraints on option prices. The call option values are then constructed using daily Standard and Poor's 500 index options. The findings suggest that entropy pricing with higher‐order moment constraints provides higher forecasting accuracy.

Journal

The Journal of Futures MarketsWiley

Published: Oct 1, 2022

Keywords: heavy‐tailed density; maximum entropy; option pricing; risk‐neutral moments

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