A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets

This paper provides comparative theoretical and numerical results on risks, values, and hedging strategies for local risk-minimization versus mean-variance hedging in a class of stochastic volatility models. We explain the theory for both hedging approaches in a general framework, specialize to a Markovian situation, and analyze in detail variants of the well-known Heston (1993) and Stein and Stein (1991) stochastic volatility models. Numerical results are obtained mainly by PDE and simulation methods. In addition, we take special care to check that all of our examples do satisfy the conditions required by the general theory.