The paper derives a parsimonious two-component affine diffusion model for a world stock index to capture the dynamics of aggregate wealth. The observable state variables of the model are the normalized index and the inverse of the stochastic market activity, both modeled as square root...

The paper derives a parsimonious two-component affine diffusion model with one driving Brownian motion to capture the dynamics of oil prices. It can be observed that the oil price behaves in some sense similarly to the US dollar. However, there are also clear differences. To identify these the...

The paper discusses the problem of hedging not perfectly replicable contingent claims by using a benchmark, the numerraire portfolio, as reference unit. The proposed concept of benchmarked risk minimization generalizes classical risk minimization, pioneered by Follmer, Sondermann and Schweizer....

This paper derives explicit formulas for both the small and large time limits of the implied volatility in the minimal market model. It is shown that interest rates do impact on the implied volatility in the long run even though they are negligible in the short time limit.

This paper makes use of an integrated benchmark modeling framework that allows us to derive term structure equations for bond and forward prices. The benchmark or numeraire is chosen to be the growth optimal portfolio (GOP). For deterministic short rate the solution of the bond term structure...

This paper makes use of an integrated benchmark modeling framework that allows us to derive term structure equations for bond and forward prices. The benchmark or numeraire is chosen to be the growth optimal portfolio (GOP). For deterministic short rate the solution of the bond term structure...