# The minimum-entropy algorithm and related methods for calibrating asset-pricing models

### Marco Avellaneda

## Abstract

We describe an algorithm for calibrating asset-pricing models based on minimizing the relative entropy between probabilities. The algorithm determines a probability measure on path-space which minimizes the Kullback information with respect to a given prior and satisfies a finite number of moment constraints which correspond to fitting prices. It admits, generically, a unique, stable, solution that depends smoothly on the input prices. We study the sensitivities of the model values of contingent claims to variations in the input prices. We find that hedge ratios can be interpreted as "risk-neutral" regression coefficients of the contingent claim's payoff on the set of payoffs of the input instruments. We also show that the minimum-entropy algorithm is a special case of a general class of algorithms for calibrating asset-pricing models based on stochastic control and convex optimization. As an illustration, we use minimum-entropy to construct a smooth curve of instantaneous forward rates from US LIBOR data and to study the corresponding sensitivities of fixed-income securities to variations in input prices.