Comonotonic Monte Carlo and its applications in option pricing and quantification of risk

Monte Carlo (MC) simulation is a technique that provides approximate solutions to a broad range of mathematical problems. A drawback of the method is its high computational cost, especially in a high-dimensional setting. Estimating the Tail Value-at-Risk for large portfolios or pricing basket options and Asian options for instance can be quite time-consuming. For these types of problems, one can construct an upper bound in the convex order by replacing the copula by the comonotonic copula. This comonotonic upper bound can be computed very quickly, but it gives only a rough approximation. In this paper we introduce the Comonotonic Monte Carlo (CoMC) simulation, which uses the best features of both approaches. By using the comonotonic approximation as a control variate we get more accurate estimates and hence the simulation is less time-consuming. The CoMC is of broad applicability and numerical results show a remarkable speed improvement. We illustrate the method for estimating Tail Value-at-Risk and pricing basket options and Asian options