Error analysis of finite difference and Markov chain approximations for option pricing

Mijatovi? and Pistorius proposed an efficient Markov chain approximation method for pricing European and barrier options in general one‐dimensional Markovian models. However, sharp convergence rates of this method for realistic financial payoffs, which are nonsmooth, are rarely available. In this paper, we solve this problem for general one‐dimensional diffusion models, which play a fundamental role in financial applications. For such models, the Markov chain approximation method is equivalent to the method of lines using the central difference. Our analysis is based on the spectral representation of the exact solution and the approximate solution. By establishing the convergence rate for the eigenvalues and the eigenfunctions, we obtain sharp convergence rates for the transition density and the price of options with nonsmooth payoffs. In particular, we show that for call‐/put‐type payoffs, convergence is second order, while for digital‐type payoffs, convergence is generally only first order. Furthermore, we provide theoretical justification for two well‐known smoothing techniques that can restore second‐order convergence for digital‐type payoffs and explain oscillations observed in the convergence for options with nonsmooth payoffs. As an extension, we also establish sharp convergence rates for European options for a rich class of Markovian jump models constructed from diffusions via subordination. The theoretical estimates are confirmed using numerical examples.     

Spatial statistical modelling of insurance risk: a spatial epidemiological approach to car insurance

Spatial models, such as the Besag, York and Mollie (BYM) model, have long been used in epidemiology and disease mapping. A common research question in these subjects is modelling the number of disease events per region; here the BYM models provides a holistic framework for both covariates and dependencies between regions. We use these tools to assess the relative insurance risk associated with the policyholders geographical location. A Bayesian modelling approach is presented and an elastic net is used to reduce the large number of possible geographic covariates. The final inference is performed using Integrated Nested Laplace Approximation. The model is applied to car insurance data from If P&C Insurance together with spatially referenced covariate data of high resolution, provided by Insightone. The entire analysis is performed using freely available R-packages. Including spatial dependence when modelling the number of claims significantly improves on the result obtained using ordinary generalised linear models. However, the support for adding a spatial component to the model for claims cost is weaker.     

IPO first‐day returns: Skewness preference,investor sentiment and uncertainty underlying factors

In this paper, we investigate the initial public offering (IPO) first-day returns. Our focus is to examine the irrational component of the agent behavior towards IPO lotteries. Based on 234 French IPOs performed between 2002 and 2012, we find that IPOs with high initial returns have higher idiosyncratic skewness, turnover and momentum. This finding provides empirical evidence for investors' preference for stocks with lottery-like features and investor sentiment. In addition, we show that the skewness preference and the investor sentiment effect are stronger during periods of favorable market conditions. Our results are robust to the integration of uncertainty underlying factors.     

制度创新与广交会发展研究

广交会自1957年建成以来在各级领导关心下已经历了45年的发展壮大,取得了丰硕的成果,在国内外享有盛名。然而,由于其本身还存在不少缺陷,加之受到国内外展览业的强劲挑战,迫切要求加快广交会的改革。利用新制度经济学的基本原理,对广交会的内外环境作了详尽分析,认为广交会要保持领先地位,必须加强制度创新。     

Conditional risk measures in a bipartite market structure

In this paper, we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insurance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation, we obtain asymptotic results for conditional risk measures based on the Value-at-Risk and the Conditional Tail Expectation. These results allow us to assess the influence of an individual institution on the systemic or market risk and vice versa through a collection of conditional risk measures. For large markets, Poisson approximations of the relevant constants are provided. Differences of the conditional risk measures for an underlying homogeneous and inhomogeneous random graph are illustrated by simulations.     

Saddlepoint approximations to the mean and variance of the extended hypergeometric distribution

Conditional inference on 2 x 2 tables with fixed margins and unequal probabilities is based on the extended hypergeometric distribution. If the support of the distribution is large, exact calculation of the conditional mean and variance of the table entry may be computationally demanding. This paper proposes a single‐saddlepoint approximation to the mean and variance. While the approximation achieves acceptable accuracy for ordinary practical purposes, an alternative saddlepoint approximation is provided that gives much closer to exact results. It improves the accuracy of current approximations to up to more than four powers of ten.     

A saddlepoint approximation to the distribution of the sum of independent non‐identically uniform random variables

Calculating the probability of the corresponding significance point is important for finite sample sizes. However, it is difficult to evaluate this probability when the sample sizes are moderate to large. Under these circumstances, consideration of a more accurate approximation for the distribution function is extremely important. Herein, we performed a saddlepoint approximation in the upper tails for the distribution of the sum of independent non‐identically uniform random variables under finite sample sizes. Saddlepoint approximation results were compared with those for a normal approximation. Additionally, the order of errors of the saddlepoint approximation was derived. © 2014 The Authors. Statistica Neerlandica © 2014 VVS.     

基于高光谱曲线的马铃薯与其他主要作物光谱差异性分析

[目的]文章以马铃薯关键生长期——结薯期为测量时点,以马铃薯和玉米、大豆、水稻为研究对象,开展高光谱曲线特征差异性研究。[方法]为更好地描述马铃薯与其他作物的光谱差异,创建高光谱反射率差异性指数、高光谱一阶导数差异性指数、高光谱红边幅值差异性指数、高光谱曲率差异性指数及高光谱植被指数差异性指数。[结果](1)马铃薯与玉米、大豆、水稻3种作物光谱曲线具有明显差异,马铃薯与玉米的反射率值在480nm附近蓝色波段位置差异最显著,差异性指数值为67.866%,与大豆、水稻的最大差异性指数值分别为49.068%、57.559%,均位于550nm附近绿色波峰位置;(2)作物光谱曲线经一阶导数变换运算,马铃薯与其他作物间的光谱差异被显著放大,在近红外波段放大程度最显著;(3)马铃薯与玉米、大豆、水稻高光谱曲率差异性指数最大值均位于波长750nm附近,差异性指数值分别为78.365%、63.471%、80.882%;(4)常用植被指数中,比值植被指数、增强型植被指数可显著区分马铃薯与玉米、大豆、水稻。[结论]差异性分析结果为农作物空间分布遥感识别提供了技术支撑。     

FIRE SALES FORENSICS: MEASURING ENDOGENOUS RISK

We propose a tractable framework for quantifying the impact of loss‐triggered fire sales on portfolio risk, in a multi‐asset setting. We derive analytical expressions for the impact of fire sales on the realized volatility and correlations of asset returns in a fire sales scenario and show that our results provide a quantitative explanation for the spikes in volatility and correlations observed during such deleveraging episodes. These results are then used to develop an econometric framework for the forensic analysis of fire sales episodes, using observations of market prices. We give conditions for the identifiability of model parameters from time series of asset prices, propose a statistical test for the presence of fire sales, and an estimator for the magnitude of fire sales in each asset class. Pathwise consistency and large sample properties of the estimator are studied in the high‐frequency asymptotic regime. We illustrate our methodology by applying it to the forensic analysis of two recent deleveraging episodes: the Quant Crash of August 2007 and the Great Deleveraging following the default of Lehman Brothers in Fall 2008.