A Partially Observed Model for Micromovement of Asset Prices with Bayes Estimation via Filtering

A general micromovement model that describes transactional price behavior is proposed. The model ties the sample characteristics of micromovement and macromovement in a consistent manner. An important feature of the model is that it can be transformed to a filtering problem with counting process observations. Consequently, the complete information of price and trading time is captured and then utilized in Bayes estimation via filtering for the parameters. The filtering equations are derived. A theorem on the convergence of conditional expectation of the model is proved. A consistent recursive algorithm is constructed via the Markov chain approximation method to compute the approximate posterior and then the Bayes estimates. A simplified model and its recursive algorithm are presented in detail. Simulations show that the computed Bayes estimates converge to their true values. The algorithm is applied to one month of intraday transaction prices for Microsoft and the Bayes estimates are obtained.     

A TEST OF A GENERAL EQUILIBRIUM STOCK OPTION PRICING MODEL

An empirical version of the Cox, Ingersoll, and Ross (1985a) call option pricing model is derived, assuming execution price uncertainty in the options market. the pricing restrictions come in the form of moment conditions in the option pricing error. These can be estimated and tested using a version of the method of simulated moments (MSM). Simulation estimates, obtained by discretely approximating the risk-neutral processes of the underlying stock price and the interest rate, are substituted for analytically unknown call prices. the asymptotics and other aspects of the MSM estimator are discussed. the model is tested on transaction prices at 15-minute intervals. It substantially outperforms the Black-Scholes model. the empirical success of the Cox-Ingersoll-Ross model implies that the continuous-time interest rate implicit in synchronous transaction quotes of 90-day Treasury-bill futures contracts is an-albeit noisy-proxy for the instantaneous volatility on common stock. the process of the instantaneous volatility is found to be close to nonstationary. It is well approximated by a heteroskedastic unit-root process. With this approximation, the Cox-Ingersoll-Ross model only slightly overprices long-maturity options.     

Finding Pareto Optimal Insurance Contracts

This paper deals with on-line computation—or step-wise learning—of Pareto optimal insurance contracts. Our approach tolerates that the loss distribution might be unknown, intractable, or not well specified. Thus we accommodate fairly inexperienced parties. Losses are here simulated or observed, one at a time, and they cause iterated revisions of the premium. The mechanical and global nature of probability calculus thereby yields to more tentative, myopic procedures, possibly closer to how humans operate or reason in face of risk. Sequential revisions may also reduce the expense of insurers' time and money in seeking sufficient statistics. Emphasized below is the remarkable simplicity and stability of the resulting adaptive procedures. Special attention goes to catastrophic risks, and to subsidized or competitive insurance.     

On a stochastic approximation procedure based on averaging

Based on the idea of averaging a new stochastic approximation algorithm has been proposed by Bather (1989), which shows a preferable performance for small to moderate sample sizes. In the present paper an almost sure representation is established for this procedure, which gives the optimal rate of convergence with minimal asymptotic variance. Work partly supported by the research grant Ku719/2-1 of the Deutsche Forschungsgemeinschaft     

Lagrange插值多项式平均算子的逼近

本文引入以第二类 Chebyshev 多项式 U_n(x)的零点为基点的 Lagrange 插值多项式平均算子 F_n(f,x),研究用 F_n(f,x)逼近连续函数 f(x)的阶。     

Liquidity risk and arbitrage pricing theory

Classical theories of financial markets assume an infinitely liquid market and that all traders act as price takers. This theory is a good approximation for highly liquid stocks, although even there it does not apply well for large traders or for modelling transaction costs. We extend the classical approach by formulating a new model that takes into account illiquidities. Our approach hypothesizes a stochastic supply curve for a securitys price as a function of trade size. This leads to a new definition of a self-financing trading strategy, additional restrictions on hedging strategies, and some interesting mathematical issues.Received: 1 November 2003, Mathematics Subject Classification: 60G44, 60H05, 90A09JEL Classification: G11, G12, G13Umut Çetin: This work was performed while Dr. Çetin was at the Center for Applied Mathematics, Cornell UniversityPhilip Protter: Supported in part by NSF grant DMS-0202958 and NSA grant MDA-904-03-1-0092 The authors wish to thank M. Warachka and Kiseop Lee for helpful comments, as well as the anonymous referee and Associate Editor for numerous helpful suggestions, which have made this a much improved paper.     

基于线性相位近似的SOQPSK-TG信号同步算法

SOQPSK-TG （Telemetry Group version of Shaped Offset Quadrature Phase Shift Key）具有良好的频率利用率和功率利用率,广泛应用于无线通信系统当中。在连续通信模式下,SOQPSK-TG信号的同步主要采用直接判决算法。为进一步降低算法复杂度,推导了基于线性相位近似的最大似然估计误差鉴别器,理论上分析了算法估计性能,并搭建了简化的接收模型。通过仿真证明了算法在估计性能上优于脉冲幅度调制方法,算法误码率接近理论性能。     

Lognormal Approximation of Complex Path-Dependent Pension Scheme Payoffs

Abstract

This paper analyzes an explicit return smoothing mechanism which has recently been introduced as part of a new type of pension savings contract that has been offered by Danish life insurers. We establish the payoff function implied by the return smoothing mechanism and show that its probabilistic properties are accurately approximated by a suitably adapted lognormal distribution. The quality of the lognormal approximation is explored via a range of simulation-based numerical experiments, and we point to several other potential practical applications of the paper's theoretical results.     

数理经济方法中跨期因子的推导及应用

本文给出了时间序列的离散和连续两种情形的跨期调整关系和增长率计算公式的推导过程,以及进一步利用等价无穷小关系阐明了离散与连续形式的近似关系,并显示了连续型跨期调整因子在构建理论与计量模型过程中更有优势,相对来说更为常用.