CIR Model with Jumps

Abstract

In this appendix we summarize a result from Lando [110], Appendix E — a semi-analytical solution for (15.20)

$${{G}_{{u,b}}}\left( {t,{{y}_{0}},\rho ,\bar{y}} \right)=\mathbb{E}\left\{ {\exp \left( {u\,{{y}_{t}}-\rho \int\nolimits_{0}^{t} {y\,ds} } \right){{1}_{{\left\{ {b\,{{y}_{t}}<\bar{y}} \right\}}}}} \right\},$$

which is the building block for computing European options in the JCIR model. Moreover we explore some of its properties, for example to see whether the presence of jumps leads to a different constraint than the Feller constraint in the pure CIR case.