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.     

An assessment on the quality of China’s preliminary data of quarterly GDP announcements

This article examines the quality of China’s preliminary announcements of the quarterly GDP. We modify the tests for unbiasedness and efficiency by incorporating the Fourier approximation to capture the effect of the state of the economy, and employing the Kiefer, Vogelsang and Bunzel (KVB) approach, developed by KVB in 2000 to reconstruct the tests to improve the finite sample properties. The results show that: (1) there is no enough evidence to support that the preliminary and first revised data are unbiased and efficient; (2) there exist systematic errors related to the state of the economy, and hence information about the state of the economy was not incorporated into the GDP data. Furthermore, we find that there is a possibility that these systematic errors associated with the stages of the business cycle may offset each other, and there is also a possibility that there exist offsetting errors in the underlying components of GDP.     

快速校正天波雷达电离层相位污染的改进方法

时变的电离层会对天波超视距雷达(OTHR)回波信号相位进行调制,产生相位污染,导致回波谱展宽。最大似然估计(MLE)法具有比相位梯度法更佳的污染校正效果,但计算量非常大。通过引入投影近似子空间跟踪法,提出了一种改进的MLE方法。改进方法采用递归手段估计最大特征值对应的特征向量,避免了特征值分解过程,能够显著降低计算量,污染校正效果与MLE法相当。理论分析与仿真对比表明改进方法普适性强,计算量只有MLE法的万分之一,更适合工程实现。     

一种混合多边缘型LDPC码密度进化算法

在二进制输入加性高斯白噪声信道下,研究了基于多边缘型低密度奇偶校验码（Multi-edge Low Density Parity Check,MET-LDPC）的密度进化算法。针对高斯近似算法在前期迭代中的不准确问题,提出了一种改进算法。在分析MET-LDPC码的密度进化的基础上,将全密度进化与高斯近似算法结合,通过设置切换限制条件,弥补早期迭代的不准确,提高编码阈值估计的准确性。仿真结果表明,与MET-LDPC全密度进化算法相比,所提算法可以有效提高编码阈值估计的准确性,对LDPC编码的设计有一定的参考价值。     

Bayesian Statistical Computations of Nonlinear Financial Time Series Models: A Survey with Illustrations

A survey of Bayesian statistical computations of quadratureformula, Laplace approximation, and Markov Chain Monte Carlo algorithms ispresentedand their applications to nonlinear financial time series models arediscussed.     

A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method

The authors report on the construction of a new algorithm for the weak approximation of stochastic differential equations. In this algorithm, an ODE-valued random variable whose average approximates the solution of the given stochastic differential equation is constructed by using the notion of free Lie algebras. It is proved that the classical Runge–Kutta method for ODEs is directly applicable to the ODE drawn from the random variable. In a numerical experiment, this is applied to the problem of pricing Asian options under the Heston stochastic volatility model. Compared with some other methods, this algorithm is significantly faster. This research was partly supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 15540110, 2003 and 18540113, 2006, the 21st century COE program at Graduate School of Mathematical Sciences, the University of Tokyo, and JSPS Core-to-Core Program 18005.     

A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELS

This paper gives a tree-based method for pricing American options in models where the stock price follows a general exponential Lévy process. A multinomial model for approximating the stock price process, which can be viewed as generalizing the binomial model of Cox, Ross, and Rubinstein (1979) for geometric Brownian motion, is developed. Under mild conditions, it is proved that the stock price process and the prices of American-type options on the stock, calculated from the multinomial model, converge to the corresponding prices under the continuous time Lévy process model. Explicit illustrations are given for the variance gamma model and the normal inverse Gaussian process when the option is an American put, but the procedure is applicable to a much wider class of derivatives including some path-dependent options. Our approach overcomes some practical difficulties that have previously been encountered when the Lévy process has infinite activity.     

STOCK LIQUIDATION VIA STOCHASTIC APPROXIMATION USING NASDAQ DAILY AND INTRA-DAY DATA

By focusing on computational aspects, this work is concerned with numerical methods for stock selling decision using stochastic approximation methods. Concentrating on the class of decisions depending on threshold values, an optimal stopping problem is converted to a parametric stochastic optimization problem. The algorithms are model free and are easily implementable on-line. Convergence of the algorithms is established, second moment bound of estimation error is obtained, and escape probability from a neighborhood of the true parameter is also derived. Numerical examples using both daily closing prices and intra-day data are provided to demonstrate the performance of the algorithms.     

Target volatility option pricing in the lognormal fractional SABR model

We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula of Itô's calculus yields an approximation formula for the price of a target volatility option in small time by the technique of freezing the coefficient. A decomposition formula in terms of Malliavin derivatives is also provided. Alternatively, we also derive closed form expressions for a small volatility of volatility expansion of the price of a target volatility option. Numerical experiments show the accuracy of the approximations over a reasonably wide range of parameters.     

Analysis of Error with Malliavin Calculus: Application to Hedging

The aim of this paper is to compute the quadratic error of a discrete time-hedging strategy in a complete multidimensional model. This result extends that of Gobet and Temam (2001) and Zhang (1999) . More precisely, our basic assumption is that the asset prices satisfy the d -dimensional stochastic differential equation   dXⁱ_t = Xⁱ_t ( bⁱ ( X_t ) dt +σ _{i , j} ( X_t ) dW^j_t )  . We precisely describe the risk of this strategy with respect to n , the number of rebalancing times. The rates of convergence obtained are     for any options with Lipschitz payoff and  1/ n ^1/4  for options with irregular payoff.