On non-existence of a one factor interest rate model for volatility averaged generalized Fong-Vasicek term structures

The purpose of this paper is to study the generalized Fong--Vasicek two-factor interest rate model with stochastic volatility. In this model the dispersion of the stochastic short rate (square of volatility) is assumed to be stochastic as well and it follows a non-negative process with volatility proportional to the square root of dispersion. The drift of the stochastic process for the dispersion is assumed to be in a rather general form including, in particular, linear function having one root (yielding the original Fong--Vasicek model or a cubic like function having three roots (yielding a generalized Fong--Vasicek model for description of the volatility clustering). We consider averaged bond prices with respect to the limiting distribution of stochastic dispersion. The averaged bond prices depend on time and current level of the short rate like it is the case in many popular one-factor interest rate model including in particular the Vasicek and Cox--Ingersoll-Ross model. However, as a main result of this paper we show that there is no such one-factor model yielding the same bond prices as the averaged values described above

On Stabilisation of Parametric Active Contours

Parametric active contours have been used extensively in computer vision for different tasks like segmentation and tracking. However, all parametric contours are known to suffer from the problem of frequent bunching and spacing out of curve points locally during the curve evolution. In a spline based implementation of active contours, this leads to occasional formation of loops locally, and subsequently the curve blows up due to instabilities. It has been shown earlier that in addition to usual evolution along the normal direction, the curve should also be evolved in the tangential direction for stability purposes. In this paper, we provide a mathematical basis for selecting such a suitable tangential component for stabilisation. We prove the boundedness of the evolved curve in this paper, and provide the physical significance. We demonstrate the usefulness of the proposed method with a number of experiments

Comparison of Two Numerical Methods for Computation of American Type of the Floating Strike Asian Option

We present a numerical approach for solving the free boundary problem for the Black-Scholes equation for pricing American style of floating strike Asian options. A fixed domain transformation of the free boundary problem into a parabolic equation defined on a fixed spatial domain is performed. As a result a nonlinear time-dependent term is involved in the resulting equation. Two new numerical algorithms are proposed. In the first algorithm a predictor-corrector scheme is used. The second one is based on the Newton method. Computational experiments, confirming the accuracy of the algorithms are presented and discussed.

On stabilisation of parametric active contours

Parametric active contours have been used extensively in computer vision for different tasks like segmentation and tracking. However, all parametric contours are known to suffer from the problem of frequent bunching and spacing out of curve points locally during the curve evolution. In a spline based implementation of active contours, this leads to occasional formation of loops locally, and subsequently the curve blows up due to instabilities. It has been shown earlier that in addition to usual evolution along the normal direction, the curve should also be evolved in the tangential direction for stability purposes. In this paper, we provide a mathematical basis for selecting such a suitable tangential component for stabilisation. We prove the boundedness of the evolved curve in this paper, and provide the physical significance. We demonstrate the usefulness of the proposed method with a number of experiments