Pricing Continuously Monitored Barrier Options under the SABR Model: A Closed-Form Approximation

The stochastic alpha beta rho (SABR) model introduced by Hagan et al. (2002) is widely used in both fixed income and the foreign exchange (FX) markets. Continuously monitored barrier option contracts are among the most popular derivative contracts in the FX markets. In this paper, we develop closed-form formulas to approximate various types of barrier option prices (down-and-out/in, up-and-out/in) under the SABR model. We first derive an approximate formula for the survival density. The barrier option price is the one-dimensional integral of its payoff function and the survival density, which can be easily implemented and quickly evaluated. The approximation error of the survival density is also analyzed. To the best of our knowledge, it is the first time that analytical (approximate) formulas for the survival density and the barrier option prices for the SABR model are derived. Numerical experiments demonstrate the validity and efficiency of these formulas.     

Akaike-type criteria and the reliability of inference: Model selection versus statistical model specification

Since the 1990s, the Akaike Information Criterion (AIC) and its various modifications/extensions, including BIC, have found wide applicability in econometrics as objective procedures that can be used to select parsimonious statistical models. The aim of this paper is to argue that these model selection procedures invariably give rise to unreliable inferences, primarily because their choice within a prespecified family of models (a) assumes away the problem of model validation, and (b) ignores the relevant error probabilities. This paper argues for a return to the original statistical model specification problem, as envisaged by Fisher (1922), where the task is understood as one of selecting a statistical model in such a way as to render the particular data a truly typical realization of the stochastic process specified by the model in question. The key to addressing this problem is to replace trading goodness-of-fit against parsimony with statistical adequacy as the sole criterion for when a fitted model accounts for the regularities in the data.     

Welfare costs of shifting trend inflation

This paper studies the welfare consequences of exogenous variations in trend inflation in a New Keynesian economy. Consumption and leisure respond asymmetrically to a rise and a decline in trend inflation. As a result, an increase in the variance of shocks to the trend inflation process decreases welfare not only by increasing the volatilities of consumption and leisure, but also by decreasing their average levels. I find that the welfare cost of drifting trend inflation is modest and that it comes mainly from reduced average levels of consumption and leisure, not from their increased volatilities.     

异质网络下含有相关系数的SIR传染病模型的建立和分析

在疾病传播过程中,染病者和易感者有多大的倾向接触是传染病是否流行的关键因素。为了研究相关系数在疾病传播过程中的动力学行为以及其对于传染病传播动力学特性的影响,将状态节点之间的相关系数作为动态变量,利用二元组的反卷积逼近方法,在异质网络上建立了含有相关系数的SIR传染病动力学模型,分析了系统平衡点的存在性,给出了染病者与易感者之间相关系数存在正值的条件。在泊松分布下,模拟出了平衡状态下相关系数的三维变化图。通过生物学意义,用概率的方法,给出了系统的最终规模。结果表明,通过分析含有相关系数的SIR传染病模型,得到SIR传染病模型复杂的动力学性态,即当染病者数量趋于零时,染病者与易感者之间的相关系数不为零。研究模型在控制传染病传播的动力学研究方面具有一定的参考价值。     

具有季节性和接种疫苗的元胞自动机传染病模型

为了研究基于二维元胞自动机的一类具有季节性和疫苗接种的SIR传染病模型对控制传染病的影响,利用平均场近似方法建立了非线性离散模型。对模型进行了数学分析,通过计算无病平衡点的Jacobian矩阵的谱半径,得到了无病平衡点的局部稳定性,通过数值模拟,找出了在正平衡点处染病者与元胞邻居结构δ的关系,并且考虑了不同的初始患者设置对疾病传播速度的影响,不同的接种疫苗率对疾病传播速度的影响。通过研究可知:当疾病的初始患者为中心分布时,传染病的传播速度小于初始患者为随机分布时的速度;随着接种疫苗率的增大,传染病的传播速度会减小,对初始患者为中心分布的元胞自动机影响较大。研究模型在控制传染病传播的动力学研究方面具有一定的参考价值。     

A Review of Modern Computational Algorithms for Bayesian Optimal Design

Bayesian experimental design is a fast growing area of research with many real‐world applications. As computational power has increased over the years, so has the development of simulation‐based design methods, which involve a number of algorithms, such as Markov chain Monte Carlo, sequential Monte Carlo and approximate Bayes methods, facilitating more complex design problems to be solved. The Bayesian framework provides a unified approach for incorporating prior information and/or uncertainties regarding the statistical model with a utility function which describes the experimental aims. In this paper, we provide a general overview on the concepts involved in Bayesian experimental design, and focus on describing some of the more commonly used Bayesian utility functions and methods for their estimation, as well as a number of algorithms that are used to search over the design space to find the Bayesian optimal design. We also discuss other computational strategies for further research in Bayesian optimal design.     

Solving DSGE portfolio choice models with dispersed private information

Noisy rational expectations models, in which agents have dispersed private information and extract information from an endogenous asset price, are widely used in finance. However, these linear partial equilibrium models do not fit well in modern macroeconomics that is based on non-linear dynamic general equilibrium models. We develop a method for solving a DSGE model with portfolio choice and dispersed private information. We combine and extend existing local approximation methods applied to public information DSGE settings with methods for solving noisy rational expectations models in finance with dispersed private information.     

Second-order approximation of dynamic models without the use of tensors

Several approaches to finding the second-order approximation to a dynamic model have been proposed recently. This paper differs from the existing literature in that it makes use of the Magnus and Neudecker (1999) definition of the Hessian matrix. The key result is a linear system of equations that characterizes the second-order coefficients. No use is made of multi-dimensional arrays or tensors, a practical implication of which is that it is much easier to transcribe the mathematical representation of the solution into usable computer code. Matlab code is available from http://paulklein.se/newsite/codes/codes.php; Fortran 90 code is available from http://alcor.concordia.ca/∼pgomme/.     

An application of Stein’s method to limit theorems for pairwise negative quadrant dependent random variables

Stein’s method is used to derive an error in normal approximation for sums of pairwise negative quadrant dependent random variables, but under the assumption of second moment only. This allows us to derive a central limit theorem for pairwise negative quadrant dependent random variables with Lindeberg’s condition. Research supported by Science Foundation of Zhejiang Provincial Education(no. 20060122)