Comonotonic Monte Carlo simulation 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, such as estimating the tail value at risk for large portfolios or pricing basket options and Asian options. For these types of problems, one can construct an upper bound in the convex order by replacing the copula with the comonotonic copula. This comonotonic upper bound can be computed very quickly, but it gives only a rough approximation. In this article, the authors introduce the Comonotonic Monte Carlo (CoMC) simulation by using the comonotonic approximation as a control variate. The CoMC is of broad applicability, and numerical results show a remarkable improvement in speed. The authors illustrate the method for estimating tail value at risk and pricing basket options and Asian options when the log returns follow a Black-Scholes model or a variance gamma model