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This paper develops a novel analytically tractable Neumann series of Besselfunctions representation for pricing (and hedging) European-style doublebarrier knock-out options, which can be applied to the whole class ofone-dimensional time-homogeneous diffusions even for the cases where thecorresponding transition density is not known. The proposed numerical method isshown to be efficient and simple to implement. To illustrate the flexibilityand computational power of the algorithm, we develop an extended jump todefault model that is able to capture several empirical regularities commonlyobserved in the literature.

Pricing double barrier options on homogeneous diffusions: a Neumann series of Bessel functions representation