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We compute zero-coupon bond prices in the Dothan model by solving the associated PDE using integral representations of heat kernels and Hartman-Watson distributions. We obtain several integral formulas for the price at time of a bond with maturity that complete those of the original paper of Dothan, which are shown not to always satisfy the boundary condition . [ABSTRACT FROM AUTHOR]

The solution of the Fokker–Planck equation for exponential Brownian functionals usually involves spectral expansions that are difficult to compute explicitly. In this paper, we propose a direct solution based on heat kernels and a new integral representation for the square modulus of the Gamma function. A financial application to bond pricing in the Dothan model is also presented. [ABSTRACT FROM AUTHOR]