Solvable Nonlinear Volatility Diffusion Models with Affine Drift

Details Solvable Nonlinear Volatility Diffusion Models with Affine Drift Solvable Nonlinear Volatility Diffusion Models with Affine Drift

2009-07-16

arxiv.org/abs/0907.2926v1

Economy

Quantitative Finance

Pricing of Securities

22 pages, 3 figures

Scientific paper

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 simpler underlying diffusions. We give a simple rigorous boundary classification and characterization of the newly constructed processes with respect to the martingale property. Specifically, we construct, analyse and classify three new families of nonlinear diffusion models with affine drift that arise from the squared Bessel process (the Bessel family), the CIR process (the confluent hypergeometric family), and the Ornstein-Uhlenbeck diffusion (the OU family).

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