Computing hitting time densities for CIR and OU diffusions: applications to mean-reverting models

This paper provides explicit analytical characterizations for first hitting time densities for Cox–Ingersoll–Ross (CIR) and Ornstein–Uhlenbeck (OU) diffusions in terms of relevant Sturm–Liouville eigenfunction expansions. The results are applicable to the analysis of mean-reverting CIR and OU models for interest rates, credit spreads, stochastic volatility, commodity convenience yields and other mean-reverting financial variables.