Bessel bridges decomposition with varying dimension. Applications to finance

We consider a class of stochastic processes containing the classical and well-studied class of Squared Bessel processes. Our model, however, allows the dimension be a function of the time. We first give some classical results in a larger context where a time-varying drift term can be added. Then in the non-drifted case we extend many results already proven in the case of classical Bessel processes to our context. Our deepest result is a decomposition of the Bridge process associated to this generalized squared Bessel process, much similar to the much celebrated result of J. Pitman and M. Yor. On a more practical point of view, we give a methodology to compute the Laplace transform of additive functionals of our process and the associated bridge. This permits in particular to get directly access to the joint distribution of the value at t of the process and its integral. We finally give some financial applications to illustrate the panel of applications of our results

Bounds for the price of discrete arithmetic Asian options.

In this paper the pricing of European-style discrete arithmetic Asian options with fixed and floating strike is studied by deriving analytical lower and upper bounds. In our approach we use a general technique for deriving upper (and lower) bounds for stop-loss premiums of sums of dependent random variables, as explained in Kaas, Dhaene and Goovaerts (2000), and additionally, the ideas of Rogers and Shi (1995) and of Nielsen and Sandmann (2003). We are able to create a unifying framework for discrete Asian options through these bounds, that generalizes several approaches in the literature as well as improves the existing results. We obtain analytical and easily computable bounds. The aim of the paper is to formulate an advice of the appropriate choice of the bounds given the parameters, investigate the effect of different conditioning variables and compare their efficiency numerically. Several sets of numerical results are included. We also show that the hedging using these bounds is possible. Moreover, our methods are applicable to a wide range of (pricing) problems involving a sum of dependent random variables.Asian option; Choice; Efficiency; Framework; Hedging; Methods; Options; Premium; Pricing; Problems; Random variables; Research; Stop-loss premium; Variables;

Bounds for stop-loss premiums of stochastic sums (with applications to life contingencies).

In this paper we present in a general setting lower and upper bounds for the stop-loss premium of a (stochastic) sum of dependent random variables. Therefore, use is made of the methodology of comonotonic variables and the convex ordering of risks, introduced by Kaas et al. (2000) and Dhaene et al. (2002a, 2002b), combined with actuarial conditioning. The lower bound approximates very accurate the real value of the stop-loss premium. However, the comonotonic upper bounds perform rather badly for some retentions. Therefore, we construct sharper upper bounds based upon the traditional comonotonic bounds. Making use of the ideas of Rogers and Shi (1995), the first upper bound is obtained as the comonotonic lower bound plus an error term. Next this bound is refined by making the error term dependent on the retention in the stop-loss premium. Further, we study the case that the stop-loss premium can be decomposed into two parts. One part which can be evaluated exactly and another part to which comonotonic bounds are applied. As an application we study the bounds for the stop-loss premium of a random variable representing the stochastically discounted value of a series of cash flows with a fixed and stochastic time horizon. The paper ends with numerical examples illustrating the presented approximations. We apply the proposed bounds for life annuities, using Makeham's law, when also the stochastic nature of interest rates is taken into account by means of a Brownian motion.Comonotonicity; Life annuity; Stochastic time horizon; Stop-loss premium;

Quanto Implied Correlation in a Multi-Lévy Framework

In this paper we apply the multivariate construction for Lévy processes introduced by Ballotta and Bonfiglioli (2014) to propose an integrated model for the joint dynamics of FX exchange rates and asset prices. We show that the proposed construction is consistent in terms of symmetries with respect to inversion and triangulation, and provides an insight into the quanto adjustment showing that this is affected by higher order cumulants of the pure jump part of the systematic risk factor. Using the Esscher transform, we relate Quanto options to vanilla call and put options, which allows for a fast calibration method to the vanilla and the Quanto market. As Quanto products offer significant exposure to the correlation between exchange rates and asset prices, they allow access to a market implied measure of this correlation. By means of a joint calibration exercise to the CME USD denominated Quanto futures on the Nikkei 225 index and both the Nikkei 225 and USDJPY market implied volatilities, we illustrate this approach for the case in which the driving process is assumed to be a Variance Gamma process

Urban agriculture: a global analysis of the space constraint to meet urban vegetable demand

Urban agriculture (UA) has been drawing a lot of attention recently for several reasons: the majority of the world population has shifted from living in rural to urban areas; the environmental impact of agriculture is a matter of rising concern; and food insecurity, especially the accessibility of food, remains a major challenge. UA has often been proposed as a solution to some of these issues, for example by producing food in places where population density is highest, reducing transportation costs, connecting people directly to food systems and using urban areas efficiently. However, to date no study has examined how much food could actually be produced in urban areas at the global scale. Here we use a simple approach, based on different global-scale datasets, to assess to what extent UA is constrained by the existing amount of urban space. Our results suggest that UA would require roughly one third of the total global urban area to meet the global vegetable consumption of urban dwellers. This estimate does not consider how much urban area may actually be suitable and available for UA, which likely varies substantially around the world and according to the type of UA performed. Further, this global average value masks variations of more than two orders of magnitude among individual countries. The variations in the space required across countries derive mostly from variations in urban population density, and much less from variations in yields or per capita consumption. Overall, the space required is regrettably the highest where UA is most needed, i.e., in more food insecure countries. We also show that smaller urban clusters (i.e., <100 km2 each) together represent about two thirds of the global urban extent; thus UA discourse and policies should not focus on large cities exclusively, but should also target smaller urban areas that offer the greatest potential in terms of physical space

On the Existence of Shadow Prices

For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless "shadow market" that yields the same optimal strategy and utility. However, the question of whether or not this indeed holds in generality has remained elusive so far. In this paper we present a counterexample which shows that shadow prices may fail to exist. On the other hand, we prove that short selling constraints are a sufficient condition to warrant their existence, even in very general multi-currency market models with possibly discontinuous bid-ask-spreads.Comment: 14 pages, 1 figure, to appear in "Finance and Stochastics

What Drives Fitness Apps Usage? An Empirical Evaluation

Part 3: Creating Value through ApplicationsInternational audienceThe increased health problems associated with lack of physical activity is of great concern around the world. Mobile phone based fitness applications appear to be a cost effective promising solution for this problem. The aim of this study is to develop a research model that can broaden understanding of the factors that influence the user acceptance of mobile fitness apps. Drawing from Unified Theory of Acceptance and Use of Technology (UTAUT) and Elaboration Likelihood Model (ELM), we conceptualize the antecedents and moderating factors of fitness app use. We validate our model using field survey. Implications for research and practice are discussed