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....

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 thesis models commodity prices and derivatives, written on commodity prices, under the benchmark approach. Under this approach, the commodity prices are modeled under the real world probability measure while the corresponding numeraire is the numeraire portfolio (NP), which is the growth...

Although statistical term structure models provide exceptional in-sample fitting and out-of-sample forecasting of interest rates, the lack of theoretical background is criticized by academics and practitioners, such as the absent of arbitrage free. In this paper we develop a general...

In this paper distributions are identified which suitably fit log-returns of the world stock index when these are expressed in units of different currencies. By searching for a best fit in the class of symmetric generalized hyperbolic distributions the maximum likelihood estimates appear to...

Without requiring the existence of an equivalent risk-neutral probability measure this paper studies a class of one-factor local volatility function models for stock indices under a benchmark approach. It is assumed that the dynamics for a large diversified index approximates that of the growth...

This paper considers a modification of the well known constant elasticity of variance model where it is used to model the growth optimal portfolio (GOP). It is shown that, for this application, there is no equivalent risk neutral pricing measure and therefore the classical risk neutral pricing...

The analysis of diffusion processes in financial models is crucially dependent on the form of the drift and diffusion coefficient functions. A new model for a stock market index process is proposed in which the index is decomposed into an average growth process and an ergodic diffusion. The...

This paper proposes a new explanation for the smile and skewness effects in implied volatilities. Starting from a microeconomic equilibrium approach, we develop a diffusion model for stock prices explicitly incorporating the technical demand induced by hedging strategies. This leads to a...

We analyze portfolio strategies which are locally optimal, meaning that they maximize the Sharpe ratio in a general continuous time jump-diffusion framework. These portfolios are characterized explicitly and compared to utility based strategies. We show that in the presence of jumps, maximizing...