Extremal behavior of stochastic volatility models

Empirical volatility changes in time and exhibits tails, which are heavier than normal. Moreover, empirical volatility has - sometimes quite substantial - upwards jumps and clusters on high levels. We investigate classical and non-classical stochastic volatility models with respect to their extreme behavior. We show that classical stochastic volatility models driven by Brownian motion can model heavy tails, but obviously they are not able to model volatility jumps. Such phenomena can be modelled by Levy driven volatility processes as, for instance, by Levy driven Ornstein-Uhlenbeck models. They can capture heavy tails and volatility jumps. Also volatility clusters can be found in such models, provided the driving Levy process has regularly varying tails. This results then in a volatility model with similarly heavy tails. As the last class of stochastic volatility models, we investigate a continuous time GARCH(1,1) model. Driven by an arbitrary Levy process it exhibits regularly varying tails, volatility upwards jumps and clusters on high levels

Derivative pricing under the possibility of long memory in the supOU stochastic volatility model

We consider the supOU stochastic volatility model which is able to exhibit long-range dependence. For this model we give conditions for the discounted stock price to be a martingale, calculate the characteristic function, give a strip where it is analytic and discuss the use of Fourier pricing techniques. Finally, we present a concrete specification with polynomially decaying autocorrelations and calibrate it to observed market prices of plain vanilla options

Assembling Neurospheres: Dynamics of Neural Progenitor/Stem Cell Aggregation Probed Using an Optical Trap

Optical trapping (tweezing) has been used in conjunction with fluid flow technology to dissect the mechanics and spatio-temporal dynamics of how neural progenitor/stem cells (NSCs) adhere and aggregate. Hitherto unavailable information has been obtained on the most probable minimum time (∼5 s) and most probable minimum distance of approach (4–6 µm) required for irreversible adhesion of proximate cells to occur. Our experiments also allow us to study and quantify the spatial characteristics of filopodial- and membrane-mediated adhesion, and to probe the functional dynamics of NSCs to quantify a lower limit of the adhesive force by which NSCs aggregate (∼18 pN). Our findings, which we also validate by computational modeling, have important implications for the neurosphere assay: once aggregated, neurospheres cannot disassemble merely by being subjected to shaking or by thermal effects. Our findings provide quantitative affirmation to the notion that the neurosphere assay may not be a valid measure of clonality and “stemness”. Post-adhesion dynamics were also studied and oscillatory motion in filopodia-mediated adhesion was observed. Furthermore, we have also explored the effect of the removal of calcium ions: both filopodia-mediated as well as membrane-membrane adhesion were inhibited. On the other hand, F-actin disrupted the dynamics of such adhesion events such that filopodia-mediated adhesion was inhibited but not membrane-membrane adhesion

High-level dependence in time series models

We present several notions of high-level dependence for stochastic processes, which have appeared in the literature. We calculate such measures for discrete and continuous-time models, where we concentrate on time series with heavy-tailed marginals, where extremes are likely to occur in clusters. Such models include linear models and solutions to random recurrence equations; in particular, discrete and continuous-time moving average and (G)ARCH processes. To illustrate our results we present a small simulation study