Summary: Integrability by Quadratures of Pricing Equations
Claudio Albanese, Giuseppe Campolieti
January 29, 2001
Department of Mathematics, University of Toronto
Math Point Ltd., Toronto
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We introduce a canonical transformation method for finding solutions to pricing prob-
lems by quadratures. The method is systematic and allows one to derive in a unified
framework the exact solutions in the pricing literature. As an application, we construct
a new families of pricing models based on the squared Bessel process which extends the
constant-variance-of-volatility (CEV) model and is integrable by quadratures.
The main difficulty in integrating a given differential
equation lies in introducing convenient variables, which
there is no rule for finding. Therefore we must travel the
reverse path and after finding some notable substitution,
look for problems to which it can be successfully applied.
Jacobi, "Lectures on Dynamics", 1847.