Transformations of Markov Processes and Classification Scheme for Solvable Driftless Diffusions
2009, v.15, №4, 563-574
Analytically tractable driftless diffusions, such as geometric Brownian motion, constant elasticity of variance (CEV) process and processes with quadratic volatility, are the main building blocks in various derivative pricing models in Mathematical Finance. All these processes share an important analytical property: the corresponding backward Kolmogorov equation can be solved explicitly by a reduction to the hypergeometric equation. In this article we classify all driftless diffusions which satisfy the above property. This classification scheme includes all known one-dimensional stationary driftless diffusion processes as well as new rich families of analytically tractable diffusions.
Keywords: driftless diffusions,Doob's h-transform,scale transformation,Liouville transformation,option pricing models