An expansion in the model space in the context of utility maximization

In the framework of an incomplete financial market where the stock price dynamics are modeled by a continuous semimartingale (not necessarily Markovian), an explicit second-order expansion formula for the power investor’s value function—seen as a function of the underlying market price of risk process—is provided. This allows us to provide first-order approximations of the optimal primal and dual controls. Two specific calibrated numerical examples illustrating the accuracy of the method are also given.     

A risk-neutral equilibrium leading to uncertain volatility pricing

We study the formation of derivative prices in an equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with worst-case aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.     

Chebyshev interpolation for parametric option pricing

Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real time. We concentrate on parametric option pricing (POP) as a generic instance of parametric conditional expectations and show that polynomial interpolation in the parameter space promises to considerably reduce run-times while maintaining accuracy. The attractive properties of Chebyshev interpolation and its tensorized extension enable us to identify broadly applicable criteria for (sub)exponential convergence and explicit error bounds. The method is most promising when the computation of the prices is most challenging. We therefore investigate its combination with Monte Carlo simulation and analyze the effect of (stochastic) approximations of the interpolation. For a wide and important range of problems, the Chebyshev method turns out to be more efficient than parametric multilevel Monte Carlo. We conclude with a numerical efficiency study.     

Explosion in the quasi-Gaussian HJM model

We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low-dimensional Markovian representation which simplifies their numerical implementation and simulation. We show rigorously that the short rate in these models explodes in finite time with positive probability, under certain assumptions for the model parameters, and that the explosion occurs in finite time with probability one under some stronger assumptions. We discuss the implications of these results for the pricing of the zero coupon bonds and Eurodollar futures under this model.     

Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations

The aim of this paper is threefold. Firstly, we study stochastic evolution equations (with the linear part of the drift being a generator of a \(C_{0}\)-semigroup) driven by an infinite-dimensional cylindrical Wiener process. In particular, we prove, under some sufficient conditions on the coefficients, the existence and uniqueness of solutions for these stochastic evolution equations in a class of Banach spaces satisfying the so-called \(H\)-condition. Moreover, we analyse the Markov property of the solutions.Secondly, we apply the abstract results obtained in the first part to prove the existence and uniqueness of solutions to the Heath–Jarrow–Morton–Musiela (HJMM) equations in weighted Lebesgue and Sobolev spaces.Finally, we study the ergodic properties of the solutions to the HJMM equations. In particular, we find a sufficient condition for the existence and uniqueness of invariant measures for the Markov semigroup associated to the HJMM equations (when the coefficients are time-independent) in the weighted Lebesgue spaces.Our paper is a modest contribution to the theory of financial models in which the short rate can be undefined.     

Does European development have Roman roots? Evidence from the German Limes

This paper contributes to the understanding of the long-run consequences of Roman rule on economic development. In ancient times, the area of contemporary Germany was divided into a Roman and a non-Roman part. The study uses this division to test whether the formerly Roman part of Germany are more developed than the non-Roman part. This is done using the Limes Germanicus wall as geographical discontinuity in a regression discontinuity design framework. The results indicate that economic development—as measured by luminosity—is indeed significantly and robustly larger in the formerly Roman part of Germany. The study identifies the persistence of the Roman road network until the present as an important factor causing this developmental advantage of the formerly Roman part of Germany both by fostering city growth and by allowing for a denser road network.     

Entrepreneurial branding: measuring consumer preferences through choice-based conjoint analysis

Start-ups face branding challenges. Not only are they confronted with the task of building brands from scratch, their newness also leads to a particularly high amount of customer uncertainty. This paper contributes to the emerging field of entrepreneurial branding by investigating start-up characteristics that signal trustworthy information to potential customers. An extended choice-based conjoint approach for modeling brand equity is used to explore the impact of different signals as initiated by established and new firms in the field of tablet computers. An empirical study reveals brand signals that have significant effects on purchase probabilities and are appropriate to overcome information asymmetries between start-ups and prospective customers.     

Survey-based forecast distributions for Euro Area growth and inflation: ensembles versus histograms

Ensemble methods can be used to construct a forecast distribution from a collection of point forecasts. They are used extensively in meteorology, but have received little direct attention in economics. In a real-time analysis of the ECB’s Survey of Professional Forecasters, we compare ensemble methods to histogram-based forecast distributions of GDP growth and inflation in the Euro Area. We find that ensembles perform very similarly to histograms, while being simpler to handle in practice. Given the wide availability of surveys that collect point forecasts but not histograms, these results suggest that ensembles deserve further investigation in economics.