ANALYTICAL SOLUTION FOR CORRELATED STOCHASTIC PROCESSES

Abstract

We develop an analytical solution for the Laplace Transform of a non necessarilyuncorrelated two-factor diffusion process integral. We exhibit the exponential affine solution of the Laplace transform calculated via Riccati differential equations. In the simulations carried out, the Laplace transform solution tracks the solution of a two correlated CIR models inferred via Monte Carlo. The result encounters applications in two real-world situations: pricing bonds via splitting the nominal interest rates as a combination of real interest rates and actual inflation, and calculating the failure probability of a engineering system.