Asymptotic approximation of the hitting-time and evaluation of a risky bond.
In this paper, we give an approximation for the density of the first–passage time through a boundary defined by smooth function S(t). The density is a solution of some Voltera integral and admits an expansion of the Neumann-type series, and the error term converges rapidly to zero. We examine the case of a non homogeneous-time Brownian diffusion which is related to the evaluation of many claims on financial asset. An application to the approximated valuation of risky bonds and options on the asset of levered firm is provided.
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