Some Integral Functionals of Reflected Sdes and Their Applications in Finance

Abstract

In this paper, we consider a class of reflected stochastic differential equations (abbr. SDEs) and we are particularly interested in some integral functionals of the solutions to the equations. We explicitly derive the Laplace transforms of those integral functionals, which are subsequently applied for the financial arguments. Here we consider a regulated market, in which the price dynamics is driven by a reflected SDE. We will calculate the conditional default probability under such price dynamics, and meanwhile we also give the pricing on some digital options. Finally, for practical purpose, an illustration for the numerical inversion of the Laplace transforms is presented in the Appendix.

Keywords: Reflected stochastic differential equation, integral functionals, Laplace transform, numerical inversion, conditional default probability, digital option

JEL Classification: G12