Closed solutions to the problem of pricing a Russian option when the stock is modeled by a diffusion with negative jumps are obtained. The Russian option is a perpetual American option on the maximum value of the stock. That stock is assumed to have the form of a Wiener process with drift and negative mixed–exponentially distributed jumps driven by a Poisson process. This result generalizes tho...

In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the integrated covariation (the covariation between the two diffusion parts, indicated by IC) from the co-jumps. This has important applications to multiple assets price modeling for forecasting, opt...

For a component or a system subject to stochastic degradation with sporadic jumps that occur at random times and have random sizes, we propose to model the cumulative degradation with random jumps using a single stochastic process based on the characteristics of Lévy subordinators, the class of non-decreasing Lévy processes. Based on an inverse Fourier transform, we derive a new closed-form rel...

In this paper, we are interested in the numerical solutions of stochastic functional differential equations (SFDEs) with jumps. Under the global Lipschitz condition, we show that the pth moment convergence of the Euler-Maruyama (EM) numerical solutions to SFDEs with jumps has order 1/p for any p ≥ 2. This is significantly different from the case of SFDEs without jumps where the order is 1/2 for...

This paper considers spot variance path estimation from datasets of intraday high frequency asset prices in the presence of diurnal variance patterns, jumps, leverage effects and microstructure noise. We rely on parametric and nonparametric methods. The estimated spot variance path can be used to extend an existing high frequency jump test statistic, to detect arrival times of jumps and to obta...

In this paper we consider two processes driven by diffusions and jumps. We consider both finite activity and infinite activity jump components. Given discrete observations we disentangle the covariation between the two diffusion parts from the co-jumps. A commonly used approach to estimate the diffusion covariation part is to take the sum of the cross products of the two processes increments; h...

Surface estimation is important in many applications. When conventional smoothing procedures, such as the running averages, local polynomial kernel smoothing procedures, and smoothing spline procedures, etc., are used for estimating jump surfaces from noisy data, jumps would be blurred at the same time when noise is removed. In recent years, new smoothing methodologies have been proposed in the...

Lateralisation of responses to presentation of a simulated predator was investigated in three species of toads: two European species (the common toad, Bufo bufo, and the green toad, Bufo viridis) and one species introduced to Australia from South America, the cane toad Bufo marinus . First a simulated snake was presented moving rapidly towards the toad in the frontal field of vision and the toa...

Expectations may be for both legs to function identically during single- and double-leg vertical jumps. However, several reasons might prevent this from occurring. The goals of this investigation were twofold: assess the presence of side-to-side jump height differences during single-leg jumps in a homogenous group of healthy subjects and determine if those with a jump height asymmetry possessed...

To understand the jumping mechanisms and strategies of adult caddis flies, leg morphology and movements were analysed in three species with mean masses of 3.9 to 38 mg. Two distinct jumping strategies were found. First (67% of 90 jumps), take-off was propelled solely by the middle and hind legs while the wings remained closed. Second (33% of jumps), the same leg movements were combined with win...