Stefan Kassberger

Efficient and robust portfolio optimization in the multivariate Generalized Hyperbolic framework

In this paper, we apply the multivariate Generalized Hyperbolic (mGH) distribution to portfolio modelling, using Conditional Value at Risk (CVaR) as a risk measure. Exploiting the fact that portfolios whose constituents follow an mGH distribution are univariate GH distributed, we prove some results relating to measurement and decomposition of portfolio risk, and show how to efficiently tackle portfolio optimization. Moreover, we develop a robust portfolio optimization approach in the mGH framework, using Worst Case Conditional Value at Risk (WCVaR) as risk measure.

Minimal q-entropy martingale measures for exponential time-changed Lévy processes

We consider structure preserving measure transforms for time-changed Lévy processes. Within this class of transforms preserving the time-changed Lévy structure, we derive equivalent martingale measures minimizing relative q-entropy. They combine the corresponding transform for the Lévy process with an Esscher transform on the time change. Structure preservation is found to be an inherent property of minimal q-entropy martingale measures under continuous time changes, whereas it imposes an additional restriction for discontinuous time changes.

When are path-dependent payoffs suboptimal?

Generalizing a result by Cox and Leland (2000) and Vanduffel et al. (2009), this note shows that risk-averse investors with fixed planning horizon prefer path-independent payoffs in any financial market if the pricing kernel is a function of the underlying’s price at the end of the planning horizon. Generally, for every payoff which is not a function of the pricing kernel, there is a more attractive alternative that depends solely on the pricing kernel at the end of the planning horizon.

q-Optimal Martingale Measures for Exponential Lévy Processes

In a multidimensional exponential Levy setting, we consider equivalent martingale measures minimizing generalized relative entropy. A family of generalized entropies corresponding to all q-optimal martingale measures is investigated in a unified way. Restricting the jump sizes of the Radon-Nikodým derivative, equivalent martingale measures which minimize generalized entropy can be obtained in cases where they do not exist otherwise. We construct these martingale measures in terms of the Radon-Nikodým derivative and the characteristic triplet of the Levy process and show that they preserve the Levy property. Further, their relation to the Esscher transform and an extension to time-changed Levy processes is discussed.

Credit Modeling Under Jump Diffusions With Exponentially Distributed Jumps — Stable Calibration, Dynamics And Gap Risk

This paper investigates a structural credit default model that is based on a hyper-exponential jump diffusion process for the value of the firm. For credit default swap prices and other quantities of interest, explicit expressions for the corresponding Laplace transforms are derived. The time-dynamics of the model are studied, particularly the jumps in credit spreads, the understanding of which is crucial e.g. for the pricing of gap risk. As an application of our findings, the model is calibrated to credit default swap spreads observed in the market.

Sharing and growth in general random multiplicative environments

We extend the discrete-time cooperation evolution model proposed by Yaari and Solomon (2010) to a version with independent multiplicative random increments of arbitrary distribution and we develop a model in continuous time driven by exponential Levy processes. In all settings, we prove that members of a sharing group enjoy a higher growth rate of their wealth and at the same time drastically reduce their exposure to random fluctuations: as more members join the group, the wealth of each member uniformly converges to a deterministic process growing at the highest possible rate. Thus, joining a sufficiently large sharing group may promise all its members to succeed almost surely even in environments where non-sharing individuals cannot escape misery on their own.

Utility-Efficient Payoffs

We show how to improve payoffs such that any portfolio composed of contracts with the improved payoffs is more attractive than the corresponding portfolio with the original payoffs.Starting from an axiomatic characterisation, we derive an amelioration operator that yields payoffs attractive to both risk averse buyers and sellers of financial contracts, including individuals with robust Savage preferences. For comparison with our approach, we briefly recall and slightly generalise core results on expected utility optimisation and cost-efficient payoffs.Furthermore, we obtain a new variant of the axiomatic characterisation of pricing operators and show that ameliorated payoffs do not admit generalised statistical arbitrage.