Decreasing Absolute Risk Aversion and Option Pricing Bounds

In this paper efficient bounds for the price of a call option are obtained using the decreasing absolute risk aversion (DARA) dominance rule. Such lower and upper bounds are obtained minimizing and maximizing, respectively, the objective function of a nonlinear optimization problem. An explicit formula (related to an exponential utility function) is given for the special case of three states of nature.

A large number of experiments have been carried out and the numerical results support the conjecture that the same formula holds for problems with a number of states n < 3. Moreover, DARA bounds are more efficient than the bounds obtained using different criteria.