Maximum Entropy in Option Pricing: A Convex-Spline Smoothing Method
✍ Scribed by Weiyu Guo
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 160 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0270-7314
- DOI
- 10.1002/fut.1902
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Applying the principle of maximum entropy (PME) to infer an implied probability density from option
prices is appealing from a theoretical standpoint because the resulting density will be the least prejudiced
estimate, as “it will be maximally noncommittal with respect to missing or unknown
information.”1 Buchen and Kelly (1996) showed that, with a set of
well‐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 is
added to the simulated option prices, the MED poorly fits the exact distribution. Motivated by the
characteristic that a call price is a convex function of the option's strike price, this study suggests a
simple convex‐spline procedure to reduce the impact of noise on observed option prices before inferring
the MED. Numerical examples show that the convex‐spline smoothing method yields satisfactory empirical
results that are consistent with prior studies. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark
21:819–832, 2001