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.     

The determinants of employers’ use of temporary contracts in the frictional labor market

This paper focuses on the following two primary reasons that employers use temporary contracts: to flexibly adjust employment and to screen workers. A search-matching framework is used to not only address employers’ endogenous choices in using temporary contracts, but also numerically identify the situations in which these contracts are likely to be used as a screening tool for permanent positions. This numerical exercise demonstrates that reducing employment protections in permanent jobs, reducing benefits for unemployed workers and raising the conversion probability from temporary to permanent employment will increase the relative proportion of employers who use temporary contracts as a screening device.     

Bottlenecks in ramping up public investment

A windfall in a developing economy with capital scarcity and investment adjustment costs facing a temporary windfall should be used to give more consumption to poorer present generations and to speed up development by ramping up public investment and paying off debt taking due account of the increasing inefficiency as investment gets ramped up. The optimal strategy requires negative genuine saving; the permanent income requires zero genuine saving. The optimal real consumption increments are smaller once one allows for absorption constraints resulting from Dutch disease and sluggish adjustment of ‘home-grown’ public capital.     

Optimal research and development and the cost of business cycles

While research and development (R&D) investment has been procyclical in the post-war period, recent literature suggests that the optimal path for R&D is countercyclical, and that the economy would be better off by subsidizing R&D in recessions. The objective of this paper is to analyze the welfare effects of distortions in the intertemporal allocation of R&D resources and to compare diverse policy interventions so as to improve social welfare. To this end, we introduce a calibrated dynamic stochastic general equilibrium model with Schumpeterian endogenous growth that is capable of explaining the observed procyclicality of R&D. Our results show that the cost of business cycles is lower in the decentralized economy with procyclical R&D than in the efficient allocation with countercyclical R&D. This is because the suboptimal propagation of shocks in the decentralized equilibrium offsets some of the existing steady-state distortions. In this second-best context, countercyclical R&D subsidies have no positive effect on welfare. In contrast, fiscal policies aimed at restoring the optimal steady-state produce large welfare gains.