Option price calibration from Rényi entropy

The calibration of the risk-neutral density function for the future asset price, based on the maximisation of the entropy measure of Rényi, is proposed. Whilst the conventional approach based on the use of logarithmic entropy measure fails to produce the observed power-law distribution when calibrat...

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Bibliographic Details
Published inPhysics letters. A Vol. 366; no. 4; pp. 298 - 307
Main Authors Brody, Dorje C., Buckley, Ian R.C., Constantinou, Irene C.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 02.07.2007
Subjects
Calibration
Havrda–Charvát entropy
Risk-neutral evaluation
Rényi entropy
91B44
Risk-neutral evaluation
Rényi entropy
91B24
Havrda–Charvát entropy
Calibration
54C70
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Summary:The calibration of the risk-neutral density function for the future asset price, based on the maximisation of the entropy measure of Rényi, is proposed. Whilst the conventional approach based on the use of logarithmic entropy measure fails to produce the observed power-law distribution when calibrated against option prices, the approach outlined here is shown to produce the desired form of the distribution. Procedures for the maximisation of the Rényi entropy under constraints are outlined in detail, and a number of interesting properties of the resulting power-law distributions are also derived. The result is applied to efficiently evaluate prices of path-independent derivatives.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2007.01.088