Maximum Entropy in Option Pricing: A Convex‐Spline Smoothing Method

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.