A general dimension reduction technique for derivative pricing

摘要: For a trajectory simulated from s standardized independent normal variates e = (e1 ,...,e s) � , the payoff of European option can be represented as max[g(e), 0], where function g(e) is assumed to differentiable and it relates nature derivative securities. In this paper, we develop new simulation technique by introducing an orthogonal class transformation so that g instead generated g(Ae) ,w hereA s-dimensional matrix. The matrix A optimally determined effective dimension underlying minimized, thereby enhancing quasi-Monte Carlo (QMC) method. proposed approach has advantage greater generality wide range applications long problem interest g(e). flexibility our illustrated applying two high-dimensional applications: Asian basket options call with stochastic volatility model. We benchmark method against well-known efficient algorithms have been advocated in these applications. numerical results demonstrate extremely powerful when combined QMC.