A Continuity Correction for Discrete Barrier Options

The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring instants; there are essentially no formulas for pricing these options, and even numerical pricing is difficult. We show, however, that discrete barrier options can be priced with remarkable accuracy using continuous barrier formulas by applying a simple continuity correction to the barrier. The correction shifts the barrier away from the underlying by a factor of exp(bet sig sqrt dt), where bet approx 0.5826, sig is the underlying volatility, and dt is the time between monitoring instants. The correction is justified both theoretically and experimentally.     

带形状参数Bézier曲线最小平方降阶逼近

给出了基于L2范数下用m次（m≤m）带形状参数B6zier曲线最小平方逼近n＋1次带形状参数Bézier曲线的方法,同时也考虑了c^0和C^1约束条件下的最小平方降阶逼近．通过解线性方程组可得到新的降阶逼近曲线的控制顶点,降阶逼近曲线的误差也可计算．     

Welfare implications of Calvo vs. Rotemberg-pricing assumptions

This paper compares the welfare implications of two widely used pricing assumptions in the New-Keynesian literature: Calvo-pricing vs. Rotemberg-pricing. We show that despite the strong similarities between the two assumptions to a first order of approximation, in general they might entail different welfare costs at higher order of approximation.     

Moment-based density approximations for aggregate losses

The determination of the distribution of aggregate losses is of crucial importance for an insurer. In this paper, we propose a technique for approximating the distribution of univariate and bivariate aggregate losses, which is solely based on their moments. Accordingly, this methodology can be implemented without any specific knowledge of the claim number or size distributions. The numerical examples presented herein indicate that the proposed approach constitutes a viable alternative to the commonly used recursive and FFT methods.     

Minimizing capital injections by investment and reinsurance for a piecewise deterministic reserve process model

We consider the possibility for an insurance company to rely on capital injections to bring the reserve back to a given level if it has fallen below it and study the problem of dynamically choosing the reinsurance level and the investment in the financial market in order to minimize the expected discounted total amount of capital injection. The reserve process is described by a piecewise deterministic process, where the random discontinuities are triggered by the arrival of a claim or by a change in the prices of the risky assets in which the company invests. The capital injections, combined with the specific model, make the problem non-linear and difficult to solve via an HJB approach. The emphasis here is on making the actual computation of a solution possible by value iteration combined with an approximation based on discretization. This leads to a nearly optimal solution with an approximation that can be made arbitrarily precise. Numerical results show the feasibility of the proposed approach.     

Monitoring risk in a ruin model perturbed by diffusion

We construct a nonparametric sequential test for the ruin probability and a corresponding change-point test in a risk model perturbed by diffusion. Some limiting properties are derived, which extend and improve on recent results of Conti (Stat Prob Lett 72:333–343, 2005) and Jahnke (Diploma thesis, University of Cologne, 2007). It is shown that the monitoring procedures can be designed such that the tests have an asymptotic prescribed false alarm rate (size) α and power 1. Some results from a small simulation study are also presented.     

一种新的频率规划方法

本文针对目前频率规划中存在的问题，提出了利用专家系统和改进遗传算法及分层技术等来克服手工频率规划过于烦琐和电子地图要求极高及频带紧张的障碍，从而在缺少准确电子地图的情况下，借助专家的经验和知识同时利用改进的优化算法亦能给出较准确的频率规划方案。同时提出了改进的模糊似然推理方法。此外我们开发了智能多层频率规划ＣＡＤ软件包，并给出仿真结果。     

Determining the implied volatility for American options using the QAM

This paper describes an efficient numerical procedure which may be used to determine implied volatilities for American options using the quadratic approximation method. Simulation results are presented. The procedure usually converges in five or six iterations with extreme accuracy under a wide variety of option market conditions. A comparison of American implied volatilities with European model implied volatilities indicates that significant differences may arise. This suggests that reliance on European model volatilities estimates may lead to significant pricing errors.     

Value-at-Risk computation by Fourier inversion with explicit error bounds

The Value-at-Risk of a delta–gamma approximated derivatives portfolio can be computed by numerical integration of the characteristic function. However, while the choice of parameters in any numerical integration scheme is paramount, in practice it often relies on ad hoc procedures of trial and error. For normal and multivariate t-distributed risk factors, we show how to calculate the necessary parameters for one particular integration scheme as a function of the data (the distribution of risk factors, and delta and gamma) in order to satisfy a given error tolerance. This allows for implementation in a fully automated risk management system. We also demonstrate in simulations that the method is significantly faster than the Monte Carlo method, for a given error tolerance.