Replicating portfolio approach to capital calculation

The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset–liability cash flows on a set of factors generated by a family of financial instruments that can be efficiently simulated. We provide the mathematical foundations and a novel dynamic and path-dependent RP approach for real-world and risk-neutral sampling. We show that our RP approach yields asymptotically consistent capital estimators if the chaotic representation property holds. We illustrate the tractability of the RP approach by three numerical examples.     

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.     

Improving the effectiveness of nondisclosure agreements by strengthening concept learning

Intellectual property infringements rank among the top economic crimes, even though there are mechanisms in place to prevent their occurrence. One such mechanism are nondisclosure agreements, which, however, have been reported to fail in practice. This article argues that this may be overcome by strengthening employees’ concept learning. In an experiment, we investigated whether extended nondisclosure agreements, which provide the employee with detailed explanations and examples, lead to better recognition of trade secrets as compared to a standard nondisclosure agreement or no agreement at all. It was found that the extended nondisclosure agreement indeed increased participants’ ability to judge what falls under the trade secret law, whereas the standard nondisclosure agreement showed no such effect. Furthermore, the effects of the factors ‘Involvement’, ‘Specificity’, ‘Publicity’, and ‘Purpose’ on the identification of trade secrets could be proven experimentally. Employees’ judgments of whether an information represents a trade secret seem to rely on general cognitive processes. From this follows that concept learning could be integrated into systematic approaches for protecting intellectual property.     

THE DYNAMICS OF REAL EXCHANGE RATES: A RECONSIDERATION

In this paper we offer a bootstrap‐based version of the Cox specification test for non‐nested hypothesis to discriminate between ESTAR and MSAR models. Both models are commonly used for modeling real exchange rates dynamics. We show that the test has good size and power properties in finite samples. In an application, we analyze several major real exchange rates to shed light on the question of which model describes these processes best. This allows us to draw conclusions about the driving forces of real exchange rates. Copyright © 2013 John Wiley & Sons, Ltd.     

Endogenous Property Rights in a Hold‐up Experiment

In a hold‐up experiment designed to test theoretical predictions following from Hart and deMeza and Lockwood regarding investment behavior, Sonnemans, Oosterbeek and Sloof (SOS) find only a partial confirmation of theory. According to SOS these deviations from standard theory can be explained by positive reciprocal behavior. In this paper, we replicate the experiment by SOS and add another group of treatments in which asset ownership is endogenized by auctioning off the assets. Our experiment shows that the results by SOS crucially depend on the ownership structure being exogenously assigned by the experimenter. We present experimental evidence that, by and large, corroborates the theoretical predictions made by Hart.     

Trade and the Environment: The Role of Firm Heterogeneity

In this paper, we derive a new effect of trade liberalization on the quality of the environment. We show that in the presence of heterogeneous firms, the aggregate volume of emissions is influenced by a reallocation effect resulting from an increase in the relative size of more productive firms. The relative importance of this reallocation effect and the scale effect well‐known from the literature is affected by the emission intensity at the firm level. Domestic emissions decrease as a result of a unilateral tariff reduction if and only if firm‐specific emission intensity decreases strongly with increasing firm productivity. As a result of the induced change in foreign emissions, domestic pollution can increase even if domestic emissions decrease.