Term Structure Models Driven by Wiener Processes and Poisson Measures: Existence and Positivity

In the spirit of [T. Björk et al., Finance Stoch., 1 (1997), pp. 141–174], we investigate term structure models driven by Wiener processes and Poisson measures with forward curve dependent volatilities. This includes a full existence and uniqueness proof for the corresponding Heath–Jarrow–Morton-type term structure equation. Furthermore, we characterize positivity preserving models by means of the characteristic coefficients. A key role in our investigation is played by the method of the moving frame, which allows us to transform term structure equations to time-dependent SDEs.