Small-noise limit of the quasi-Gaussian log-normal HJM model

Quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low dimensional Markovian representation, which greatly simplifies their numerical implementation. We present a qualitative study of the solutions of the quasi-Gaussian log-normal HJM model. Using a small-noise deterministic limit we show that the short rate may explode to infinity in finite time. This implies the explosion of the Eurodollar futures prices in this model. We derive explicit explosion criteria under mild assumptions on the shape of the yield curve.     

On Gaussian HJM framework for Eurodollar Futures

One of the standard tools for the theoretical analysis of fixed income securities and their associated derivatives is the term structure model of Heath, Jarrow and Morton. In this paper the question, what specific HJM model is consistent with the observed price of an Eurodollar Futures contract? is discussed. Eurodollar Futures, apart from being the most heavily traded futures are connected to London Inter Bank Offered Rate (LIBOR) and to domestic monetary conditions. The answer to the above question will help in pricing any new derivative on Eurodollar Futures or the one that is not heavily traded. A simple tool to measure the adequacy of different HJM structures that may be used to model Eurodollar Futures price process is suggested. Moreover, the question of estimation of parameters of these models by different methods—method of realized volatility, method of maximum likelihood (ML) and a two‐stage method that combines both the realized volatility and ML—is addressed. Although it sounds like a typical statistical procedure, one must be careful in applying standard statistical techniques that are not suitable under arbitrage theory, in particular, ML method. Copyright © 2010 John Wiley & Sons, Ltd.     

Eurodollar futures pricing in log-normal interest rate models in discrete time

We demonstrate the appearance of explosions in three quantities in interest rate models with log-normally distributed rates in discrete time. (1) The expectation of the money market account in the Black, Derman, Toy model, (2) the prices of Eurodollar futures contracts in a model with log-normally distributed rates in the terminal measure and (3) the prices of Eurodollar futures contracts in the one-factor log-normal Libor market model (LMM). We derive exact upper and lower bounds on the prices and on the standard deviation of the Monte Carlo pricing of Eurodollar futures in the one factor log-normal Libor market model. These bounds explode at a non-zero value of volatility, and thus imply a limitation on the applicability of the LMM and on its Monte Carlo simulation to sufficiently low volatilities.     

Volatility of volatility of financial markets

We present empirical evidence for considering volatility of Eurodollar futures as a stochastic process, requiring a generalization of the standard Black-Scholes (BS) model which treats volatility as a constant. We use a previous development of a statistical mechanics of financial markets (SMFM) to model these issues.     

A Theoretically Consistent Version of the Nelson and Siegel Class of Yield Curve Models

A popular class of yield curve models is based on the Nelson and Siegel approach of ‘fitting’ yield curve data with simple functions of maturity. However, such models cannot be consistent across time. This article addresses that deficiency by deriving an intertemporally consistent and arbitrage‐free version of the Nelson and Siegel model. Adding this theoretical consistency expands the potential applications of the Nelson and Siegel approach to exercises involving a time‐series context, such as forecasting the yield curve and pricing interest rate derivatives. As a practical example, the intertemporal consistency of the model is exploited to derive a theoretical framework for forecasting the yield curve. The empirical application of that framework to United States data results in out‐of‐sample forecasts that outperform the random walk over the sample period of almost 50 years, for forecast horizons ranging from six months to three years.     

Curve forecasting by functional autoregression

This paper deals with the prediction of curve-valued autoregression processes. It develops a novel technique, predictive factor decomposition, for the estimation of the autoregression operator. The technique is based on finding a reduced-rank approximation to the autoregression operator that minimizes the expected squared norm of the prediction error.Implementing this idea, we relate the operator approximation problem to the singular value decomposition of a combination of cross-covariance and covariance operators. We develop an estimation method based on regularization of the empirical counterpart of this singular value decomposition, prove its consistency and evaluate convergence rates.The method is illustrated by an example of the term structure of the Eurodollar futures rates. In the sample corresponding to the period of normal growth, the predictive factor technique outperforms the principal components method and performs on a par with custom-designed prediction methods.     

On the Spurious Correlation Between Sample Betas and Mean Returns

Abstract

Cornerstone asset pricing models, such as capital asset pricing model (CAPM) and arbitrage pricing theory (APT), yield theoretical predictions about the relationship between expected returns and exposure to systematic risk, as measured by beta(s). Numerous studies have investigated the empirical validity of these models. We show that even if no relationship holds between true expected returns and betas in the population, the existence of low-probability extreme outcomes induces a spurious correlation between the sample means and the sample betas. Moreover, the magnitude of this purely spurious correlation is similar to the empirically documented correlation, and the regression slopes and intercepts are very similar as well. This result does not necessarily constitute evidence against the theoretical asset pricing models, but it does shed new light on previous empirical results, and it points to an issue that should be carefully considered in the empirical testing of these models. The analysis points to the dangers of relying on simple least squares regression for drawing conclusions about the validity of equilibrium pricing models.     

Is prediction possible? Chaotic behavior of Multiple Equilibria Regulation Model in cellular automata topology

In this article, we present the Multiple Equilibria Regulation (MER) Model in cellular automata topology. As argued in previous explorations of the model, for certain parameter values, the behavior of the system exhibits transient chaos (namely, the system is unpredictable but ends in a final steady state). In order to approach empirical reality, we introduce a cellular automata topology. Examining the outcome of the simulations leads us to conclude that for certain parameter values tested, the system yields chaotic behavior. Thus, cellular automata contribution has proven crucial, because the introduced topology converts the behavior of the system from transient chaos to “pure” chaos, i.e., the system is not only unpredictable on the long run but, in addition, it will never rest in a final steady state. According to these findings, authors argue the theoretical hypothesis that the urge for “prediction” in social sciences should be reconsidered in terms of “predictability horizon”. © 2004 Wiley Periodicals, Inc. Complexity 10: 23–36, 2004     

Optimization of the number of components in the mixed model using multi-criteria decision-making

The distributions of empirical data are often complex. Such complexity cannot be sufficiently addressed by the individual theoretical statistical distribution function. Furthermore, the selection of the distribution function becomes more complicated when the empirical data present a multi-peak feature. In such a case, the multiple testing criteria and the mixed model must be considered during the selection of an appropriate distribution function. Aiming at this vague challenge, the present paper proposes a novel method for establishing a mixed model that can describe accurately the distribution characteristics of empirical data. Apart from combining the Akike and Bayesian information criteria to define the feasible solutions of the mixed model, this study also utilizes the root mean squared deviation, coefficient of determination, Kolmogorov–Smirnov test statistic, average deviation in cumulative distribution function, and average deviation in probability distribution function as the testing criteria. In addition, a non-linear programming is used to find the weighting factors of each criterion. The multi-criteria decision-making technology is adopted to comprehensively and objectively integrate these testing criteria into a synthetic indicator. Finally, an optimization algorithm is proposed to determine the optimal number of components in the mixed model. The illustrated results of the simulated data and measured signals confirm that this approach can estimate precisely the number of components as well as establish a highly accurate mixed model.     

Differentially Private Precision Matrix Estimation

In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by using the alternating direction method of multipliers (ADMM) algorithm. Furthermore, we prove theoretical results showing that the differentially private ridge estimator for the precision matrix is consistent under fixed-dimension asymptotic, and establish a convergence rate of differentially private graphical lasso estimator in the Frobenius norm as both data dimension p and sample size n are allowed to grow. The empirical results that show the utility of the proposed methods are also provided.     

基于便利收益的商品期货套期保值策略研究

依据便利收益是商品现货与期货长期均衡关系的主要影响因素,研究商品便利收益对商品期货套期保值策略的影响。通过求解最大化期望效用的套期保值决策模型,得到了最优套期保值比率的封闭解,并且提出了以便利收益为修正因子的ECT-GARCH模型,同时选取2005年01月到2013年10月期间沪铝现货和期货数据进行实证分析。研究发现:便利收益的波动性与套期保值比率呈负相关,在套期保值比率估计精度和套期保值绩效方面,ECT-GARCH模型均优于B-GARCH模型和ECM-GARCH模型。     

Competing trade mechanisms and monotone mechanism choice

We investigate the choice between posted prices and auctions of competing sellers with private valuations. Assuming that buyers face higher hassle costs in auctions, we show the existence of monotone pure strategy equilibria where sellers offer posted prices rather than auctions if and only if they have a sufficiently high reservation value. Posted prices sell with lower probability but yield a larger revenue in case of trade. Using an empirical strategy to compare revenues of posted prices and auctions that takes selling probabilities explicitly into account, we find our theoretical predictions supported by data from eBay auctions on ticket sales for the EURO 2008 European Football Championship.     

中国社会保障支出与消费水平关系研究——基于非线性STR模型的实证分析

针对现有社会保障支出与消费水平关系实证研究中存在的不足,应用时间序列的非线性STR模型验证了1952-2009年期间我国财政社保支出与消费水平非线性关系的存在.研究结论表明二者问呈显著的负相关关系,且呈现出明显的阶段性特征,并在线性和非线性间频繁转换.具体可分为三个主要阶段,1958-1963年为负向非线性关系,1964 1978年二者关系则很不显著;1979年至今又重新转变为负向非线性关系.这些结论为我国制定和实施社会保障支出政策提供了现实的理论依据.     

双侧伽马期权定价与B-S模型的比较研究

本文首次运用双侧伽马分布对上证50ETF期权定价进行实证研究,并与经典的B-S模型进行比较。实证结果表明:采用双侧伽马模型来估算期权的理论价格,无论是在95%置信区间下还是在99%置信区间下,双侧伽马模型对于期权价格的测定都要优于B-S模型期权定价,因此,双侧伽马模型可以作为B-S模型的一种改进。     

Optimal hedging under output price uncertainty

This paper provides a theoretical and empirical analysis of optimal hedging under output price uncertainty. The theoretical analysis is facilitated by exploiting the duality between production and cost while the empirical implementation uses the envelope theorem and the indirect expected utility function. Empirically estimable equations are derived by approximating the indirect expected utility function by a Taylor series approximation. The model is tested by using live cattle data as output while using prices of corn, soybeans, and the feeder cattle as inputs. The results support the theoretical predictions and the evidence shows that live cattle farmers exhibit decreasing absolute risk aversion.     

Lognormality of rates and term structure models

A term structure model with lognormal type volatility structure is proposed. The Heath, Jarrow and Morton (HJM) framework, coupled with the theory of stochastic evolution equations in infinite dimensions, is used to show that the resulting instantaneous rates are well defined (they do not explode) and remain positive, contrary to those derived in [2]. They are also bounded from below and above by lognormal processes. The model can be used to price and hedge caps, swaptions and other interest rate and currency derivatives including the Eurodollar futures contract, which requires integrability of one over zero coupon bond. This extends results obtained by Sandmann and Sondermann in [22] and [23] for Markovian lognormal short rates to (non-Markovian) lognormal forward rates. We show also existence of invariant measures for the proposed term structure dynamics     

风险资产市场组合的概率分布和均值估计

探讨CAPM中风险资产市场组合的概率分布和均值估计问题.在股票价格行为模型用维纳过程(又称布朗运动)表述的前提下,证明了CAPM中的市场组合服从加法逻辑正态分布的结论,进而给出了市场组合均值的3种估计.以此为基础进行CAPM的实证检验,才具有理论上的严密性.     

FISHING YIELD,CURVATURE AND SPATIAL BEHAVIOR: IMPLICATIONS FOR MODELING MARINE RESERVES

ABSTRACT. Given a paucity of empirical data, policymakers are forced to rely on modeling to assess potential impacts of creating marine reserves to manage fisheries. Many modeling studies of reserves conclude that fishing yield will increase (or decrease only modestly) after creating a reserve in a heavily exploited fishery. However, much of the marine reserves modeling ignores the spatial heterogeneity of fishing behavior. Contrary to empirical findings in fisheries science and economics, most models assume explicitly or implicitly that fishing effort is distributed uniformly over space. This paper demonstrates that by ignoring this heterogeneity, yield‐per‐recruit models systematically overstate the yield gains (or understate the losses) from creating a reserve in a heavily exploited fishery. Conversely, at very low levels of exploitation, models that ignore heterogeneous fishing effort overstate the fishing yield losses from creating a reserve. Starting with a standard yield‐per‐recruit model, the paper derives a yield surface that maps spatially differentiated fishing effort into total long‐run fishing yield. It is the curvature of this surface that accounts for why the spatial distribution of fishing effort so greatly affects predicted changes from forming a reserve. The results apply generally to any model in which the long‐run fishing yield has similar curvature to a two‐patch Beverton‐Holt model. A simulation of marine reserve formation in the California red sea urchin fishery with Beverton‐Holt recruitment, eleven patches, and common larval pool dispersal dynamics reinforces these results.     

Consistent estimation and testing in heteroscedastic polynomial errors-in-variables models

The paper concentrates on consistent estimation and testing in functional polynomial measurement errors models with known heterogeneous variances. We rest on the corrected score methodology which allows the derivation of consistent and asymptotically normal estimators for line parameters and also consistent estimators for the asymptotic covariance matrix. Hence, Wald and score type statistics can be proposed for testing the hypothesis of a reduced linear relationship, for example, with asymptotic chi-square distribution which guarantees correct asymptotic significance levels. Results of small scale simulation studies are reported to illustrate the agreement between theoretical and empirical distributions of the test statistics studied. An application to a real data set is also presented.