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.     

Polycentric development in the Cape Town city-region: Empirical assessment and consideration of spatial policy implications

The concept of the ‘polycentric urban region’ has been popularised both as a theoretical concept for understanding regional urban systems in an era of reduced transport and communication costs, and as a normative policy objective in its own right. This paper explores its relevance to the rapidly urbanising Cape Town city-region. First, empirical evidence for the emergence of polycentric regional development patterns was considered. Shifts in relative settlements sizes (morphological polycentrism) over the period 1991–2011 were examined using population data, and patterns of inter-settlement interactions (functional polycentrism) were explored by analysing commuting information. Contrary to expectations, trends toward polycentric development were found to be weak. Second, the paper considers the relevance and value of polycentric development thinking for regional economic and spatial planning policy, concluding that there are insufficient grounds for policy intervention aimed at encouraging polycentric regional development or countering the dominance of Cape Town in the region.     

Potential implications of COVID-19 on the Canadian pork industry

Canada and the United States have strong economic ties and form part of an integrated North American pork industry. Canada's pork industry is export-oriented, and the United States represents a key market for both live pigs and pork. Pork value chain stakeholders include input suppliers, pig producers, transportation companies, slaughter plants, wholesalers, and retailers. There are three overriding areas of concern for the Canadian pork industry with respect to potential impacts of the current pandemic (COVID-19). The first is Canada/US trade and the ability to continue exporting Canadian live pigs and pork to the United States. The second is labor and the impact of potential absenteeism on all sectors of the pork value chain. The third is global trade, because Canada's pork industry relies heavily on exporting pork to markets around the world.     

Unintended consequences in demarketing antisocial behaviour: project Bernie

Unintended consequences are recognised as a potential risk for well-intentioned social marketing interventions and as a comparatively under-researched topic in the field. This case study uses an intervention tackling deliberate grassfires to explore the application of social marketing in a novel context, its potential effectiveness in demarketing antisocial behaviours and the potential of such interventions to generate positive and negative unintended consequences. The intervention’s evaluation confirms social marketing’s potential value in tackling ingrained antisocial behaviours within communities. It also revealed unexpected benefits accruing from changes within the target community, within the sponsoring fire service and in the relationship between the two. The paper concludes by discussing the implications of potential unexpected and unplanned consequences for intervention planning, conduct and evaluation.     

The Aggregate Demand Curve and Its Proper Interpretation

Textbook authors, in their presentations of aggregate demand–aggregate supply, are admonished to set their houses in order. The writers suggest the continued usefulness of the traditional “Keynesian cross” model as a pedagogical device and present a version that they allege to be superior to the popular AD–AS models found in many contemporary texts.     

Demographic change,human capital accumulation and R&D‐based growth

Employing an overlapping generations model of R&D‐based growth with endogenous fertility and education decisions, we examine how demographic changes induced by an increase in life expectancy influence the long‐run growth rate of the economy. We demonstrate that life expectancy, when relatively low (high), positively (negatively) affects economic growth. This paper also compares the growth implications of child education subsidy policies (i.e., policies for enhancing basic education) and child rearing subsidy policies (i.e., pro‐natal policies) and demonstrate that while the child education subsidies consistently foster economic growth, child rearing subsidies may negatively affect economic growth.     

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.