Economic Hysteresis Effects and Hitting Time Densities for CIR Diffusions

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. Starting with Vasicek (1977) and Cox, Ingersoll and Ross (1985), the Gaussian Ornstein– Uhlenbeck and Feller’s (1951) square-root diffusions are among the most commonly used s...

Exact simulation of Bessel diffusions

We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and/or change of measure. All these diffusions are broadly us...

Discretely monitored first passage problems and barrier options: an eigenfunction expansion approach

This paper develops an eigenfunction expansion approach to solve discretely monitored first passage time problems for a rich class of Markov processes, including diffusions and subordinate diffusions with jumps, whose transition or Feynman-Kac semigroups possess eigenfunction expansions in L spaces. Many processes important in finance are in this class, including OU, CIR, (JD)CEV diffusions and...

Solvable Nonlinear Volatility Diffusion Models with Affine Drift

We present a method for constructing new families of solvable one-dimensional diffusions with linear drift and nonlinear diffusion coefficient functions, whose transition densities are obtainable in analytically closed-form. Our approach is based on the so-called diffusion canonical transformation method that allows us to uncover new multiparameter diffusions that are mapped onto various simple...

First Passage Time Moments of Jump-Diffusions with Markovian Switching