Measures of model uncertainty and calibrated option bounds

Recently, Cont introduced a quantitative framework for measuring model uncertainty in the context of derivative pricing [Model uncertainty and its impact on the pricing of derivative instruments, Math. Finance, 16(3) (2006), pp. 519-547]. Two measures of model uncertainty were proposed: one measure based on a coherent risk measure compatible with market prices of derivatives and another measure based on convex risk measures. We show in a discrete time, finite state probability setting, that the two measures introduced by Cont are closely related to calibrated option bounds studied recently by King et al. [Calibrated option bounds, Inf. J. Ther. Appl. Financ., 8(2) (2005), pp. 141-159]. The precise relationship is established through convex programming duality. As a result, the model uncertainty measures can be computed efficiently by solving convex programming or linear programming problems after a suitable discretization. Numerical results using S&P 500 options are given.