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Maximum Entropy in Option Pricing: A Convex‐Spline Smoothing Method
Author(s) -
Guo Weiyu
Publication year - 2001
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.1902
Subject(s) - smoothing , mathematics , entropy (arrow of time) , smoothing spline , regular polygon , probability density function , econometrics , spline (mechanical) , mathematical optimization , statistics , spline interpolation , physics , geometry , quantum mechanics , bilinear interpolation , thermodynamics
Applying the principle of maximum entropy (PME) to infer an implied probability density from optionprices is appealing from a theoretical standpoint because the resulting density will be the least prejudicedestimate, as “it will be maximally noncommittal with respect to missing or unknowninformation.”1 Buchen and Kelly (1996) showed that, with a set ofwell‐spread simulated exact‐option prices, the maximum‐entropy distribution (MED)approximates a risk‐neutral distribution to a high degree of accuracy. However, when random noise isadded to the simulated option prices, the MED poorly fits the exact distribution. Motivated by thecharacteristic that a call price is a convex function of the option's strike price, this study suggests asimple convex‐spline procedure to reduce the impact of noise on observed option prices before inferringthe MED. Numerical examples show that the convex‐spline smoothing method yields satisfactory empiricalresults that are consistent with prior studies. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark21:819–832, 2001