We investigate the existence of affine realizations for interest rate term structure models driven by Levy processes. Using as numeraire the growth optimal portfolio, we model the interest rate term structure under the real-world probability measure, and hence, we do not need the existence of an...

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.

Market models which re ect stylised properties of the interest rate term structure are widely used for modelling and pricing interest rate derivatives. We consider a market model involving the short rate and a diversied global stock index. We illustrate the stylised properties of the interest...

The growth optimal portfolio (GOP) plays an important role in finance, where it serves as the numeraire portfolio, with respect to which contingent claims can be priced under the real world probability measure. This paper models the GOP using a time dependent constant elasticity of variance...

We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization...

According to the expectations hypothesis, the forward rate is equal to the expected future short rate, an argument that is not supported by most empirical studies that demonstrate the existence of term premiums. An alternative arbitrage-free term structure model for reviewing the expectations...

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...