Maximum entropy in option pricing: A convex-spline smoothing method

Applying the principle of maximum entropy (PME) to infer an implied probabi lity 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 informat ion."(1) Buchen and Kelly (1996) showed that, with a set of well-spread sim ulated exact-option prices, the maximum-entropy distribution (MED) approxim ates a risk-neutral distribution to a high degree of accuracy. However, whe n 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 si mple convex-spline procedure to reduce the impact of noise on observed opti on prices before inferring the MED. Numerical examples show that the convex -spline smoothing method yields satisfactory empirical results that are con sistent with prior studies. (C) 2001 John Wiley & Sons, Inc.