In this paper, we present an alternative approach as a suitable framework under which liability driven investments can be valued and hedged. This benchmark approach values both assets and liabilities consistently under the real world probability measure using the best performing portfolio, the...

This paper considers a new class of Monte Carlo methods that are combined with PDE expansions for the pricing and hedging of derivative securities for multidimensional diffusion models. The proposed method combines the advantages of both PDE and Monte Carlo methods and can be directly applied to...

Many providers of variable annuities such as pension funds and life insurers seek to hedge their exposure to embedded guarantees using longdated derivatives. This paper extends the benchmark approach to price and hedge long-dated equity index options using a combination of cash, bonds and...

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.

In this paper, we discuss how to model credit risk under the benchmark approach. Firstly we introduce an affine credit risk model. We then show how to price credit default swaps (CDSs) and introduce credit valuation adjustment (CVA) as an extension of CDSs. In particular, our model can capture...

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...

This paper proposes a consistent benchmark approach to price weather derivatives. The growth optimal portfolio to price weather derivatives. The growth optimal portfolio is used as numeraire such that all benchmarked fair price processes are martingales. No measure transformation is needed for...

Monetary policy has pursued the concept of inflation targeting. This has been implemented in many countries. Here interest rates are supposed to respond to an inflation gap and output gap. Despite long term continuing growth of the world financial assets, recently, monetary policy, in particular...