Derivative pricing based on local utility maximization
In this paper a new approach to contingent claim valuation in incomplete market model is studied. The notions of local utility and neutral derivative price are introduced. Local utility optimization can be interpreted as expected utility maximization of the gains over infinitesimal time intervals. A derivative price is called neutral if the optimal portfolio contains no contingent claim. The author introduces the sensitivity process of a contingent claim. Neutral prices are based on the assumption that the net demand for derivatives is \(0\). The author measures the sensitivity of the contingent claim price to violation of this assumption by computing how much the price reacts to small demand perturbations. This sensitivity process can be used to construct price bounds and it allows to calibrate the neutral pricing model to initially observed market quotations. The illustration of neutral derivative pricing and sensitivity processes are presented by considering some particular cases such as: market with continuous path, bivariate diffusion models, the model with exponential Lévy processes and the discrete-time model.
scientific article; zbMATH DE number 1833870