Minimum Entropy Calibration of Asset-Pricing Models
Marco Avellaneda
IJTAF, 1999

---

We present an algorithm for  calibrating asset-pricing models to benchmark prices. The algorithm computes the probability that minimizes the relative entropy  with respect to a prior and satisfies and finite number of moment constraints. These constraints arise from fitting the model to the prices of benchmark instruments. Generically, there exists a unique solution which is stable, i.e. depends smoothly on the input prices. We study the sensitivities of the values of contingent claims with respect to variations  in the benchmark prices.  We find that the sensitivities can be  interpreted as regression coefficients of the payoffs of the contingent claims on the set of payoffs of the benchmark instruments, under the risk-neutral measure. 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 swap/FRA data and to study the corresponding sensitivities of fixed-income instruments  to variations in  input prices.

---