Correlated CIR processes and applications in finance and engineering
We investigate the square root diffusion process, also named the CIR process. It is a stochastic differential equation which ensures mean reversion of the state variable towards a long run level and avoids the possibility of negative values of the process. These are interesting properties for a number of practical applications, especially when two CIR processes are correlated. We developed analytical approximations to convert the correlated CIR into an affine-diffusion process to find closed-form solutions for the Laplace Transform via Riccati Equations. We apply the final result to three real-world situations: first we model the default probability of emerging market bonds issued in foreign currency, second we price bonds splitting the nominal interest rates as a combination of real interest rates and actual inflation, and lastly we calculate the reliability of an industrial loom subjected to two failure modes.
Allan Jonathan da Silva - LNCC/MCTI
Davi Michel Valladão - PUC-RJ
Jack Baczynski - Laboratório Nacional de Computação Científica - firstname.lastname@example.org
José Valentim Machado Vicente
Marcelo Dutra Fragoso - Laboratório Nacional de Computação Científica - email@example.com
Rodrigo Novinski - Instituto Brasileiro de Mercado de Capitais - firstname.lastname@example.org