Path Integrals and Smart Monte Carlo - II

Abstract

“Smart Monte Carlo” (SMC) improves accuracy and speed. We extend results in an earlier paper, applying SMC to path-dependent deals and multifactor models. Auxiliary results are a path-to-path distance, an analytic approximation for N-dimensional Gaussian integrals, and time interpolation results. We suggest “model perturbation” using simple approximate models, and introduce a new product “DIAS” for better mortgage servicing hedging. We prove a consistency condition for the MRG interest-rate model, and discuss real-world vs. risk-neutral simulations.

Keywords: Smart Monte Carlo, SMC, accuracy, speed, extend, N-dimensional Gaussian integrals, path-to-path distance, time interpolation , consistency condition, MRG interest-rate model, real-world, risk-neutral, risk-neutral,mortgage servicing, hedge

JEL Classification: C14, C63, C65, G1