arXiv subjects

Jan Kallsen

Publications and source records attributed to Jan Kallsen.

22 records · Page 2Linked to original sources

arXiv2011

On the Performance of Delta Hedging Strategies in Exponential Lévy Models

We consider the performance of non-optimal hedging strategies in exponential Lévy models. Given that both the payoff of the contingent claim and the hedging strategy admit suitable integral representations, we use the Laplace transform approach of Hubalek et al. (2006) to derive semi-explicit formulas for the resulting mean squared hedging error in terms of the cumulant generating function of the underlying Lévy process. In two numerical examples, we apply these results to compare the efficiency of the Black-Scholes hedge and the model delta to the mean-variance optimal hedge in a normal inverse Gaussian and a diffusion-extended CGMY Lévy model.

q-fin.CP↗

arXiv2010

Existence of Shadow Prices in Finite Probability Spaces

A shadow price is a process lying within the bid/ask prices of a market with proportional transaction costs, such that maximizing expected utility from consumption in the frictionless market with this price process leads to the same maximal utility as in the original market with transaction costs. For finite probability spaces, this note provides an elementary proof for the existence of such a shadow price.

q-fin.PM↗

arXiv2009

Utility maximization in models with conditionally independent increments

We consider the problem of maximizing expected utility from terminal wealth in models with stochastic factors. Using martingale methods and a conditioning argument, we determine the optimal strategy for power utility under the assumption that the increments of the asset price are independent conditionally on the factor process.

q-fin.PM↗

arXiv2006

Variance-optimal hedging for processes with stationary independent increments

We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we show that for this class of processes the optimal endowment and strategy can be expressed more explicitly. The corresponding formulas involve the moment, respectively, cumulant generating function of the underlying process and a Laplace- or Fourier-type representation of the contingent claim. An example illustrates that our formulas are fast and easy to evaluate numerically.

math.PR↗