Term structure models driven by general Lévy processes

Empirical investigations ([1], [2]) showed that purely discontinuous Lévy processes allow more realistic modeling of financial time series. We present a new class of bond price models that can be driven by a wide range of Lévy processes (Lt). We do not just replace Brownian motion (Bt) in the standard diffusion model for the price of a zero coupon bond with maturity T dP (t, T ) = P (t, T )(r(t)dt+ σ(t, T ) dBt) by (Lt). As the result we would get the Doléans-Dade exponential. Instead we introduce (Lt) in the solution of this equation, which can be written in the form