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;

Perceptual correlates of homosynaptic long-term potentiation in human nociceptive pathways: A replication study

Animal studies have shown that high-frequency stimulation (HFS) of peripheral C-fibres induces long-term potentiation (LTP) within spinal nociceptive pathways. The aim of this replication study was to assess if a perceptual correlate of LTP can be observed in humans. In 20 healthy volunteers, we applied HFS to the left or right volar forearm. Before and after applying HFS, we delivered single electrical test stimuli through the HFS electrode while a second electrode at the contra-lateral arm served as a control condition. Moreover, to test the efficacy of the HFS protocol, we quantified changes in mechanical pinprick sensitivity before and after HFS of the skin surrounding both electrodes. The perceived intensity was collected for both electrical and mechanical stimuli. After HFS, the perceived pain intensity elicited by the mechanical pinprick stimuli applied on the skin surrounding the HFS-treated site was significantly higher compared to control site (heterotopic effect). Furthermore, we found a higher perceived pain intensity for single electrical stimuli delivered to the HFS-treated site compared to the control site (homotopic effect). Whether the homotopic effect reflects a perceptual correlate of homosynaptic LTP remains to be elucidated.Fil: van de Broeke, Emanuel N.. Université Catholique de Louvain; BélgicaFil: Vanmaele, Tessa. Katholikie Universiteit Leuven; BélgicaFil: Mouraux, André. Université Catholique de Louvain; BélgicaFil: Stouffs, Alexandre. Université Catholique de Louvain; BélgicaFil: Biurrun Manresa, José Alberto. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática; ArgentinaFil: Torta, Diana M.. Katholikie Universiteit Leuven; Bélgic