Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns

In this work, we investigate sequential Bayesian estimation for inference of stochastic volatility with variance‐gamma (SVVG) jumps in returns. We develop an estimation algorithm that combines the sequential learning auxiliary particle filter with the particle learning filter. Simulation evidence and empirical estimation results indicate that this approach is able to filter latent variances, identify latent jumps in returns, and provide sequential learning about the static parameters of SVVG. We demonstrate comparative performance of the sequential algorithm and off‐line Markov Chain Monte Carlo in synthetic and real data applications.     

Global optimization of higher order moments in portfolio selection

We discuss the global optimization of the higher order moments of a portfolio of financial assets. The proposed model is an extension of the celebrated mean variance model of Markowitz. Asset returns typically exhibit excess kurtosis and are often skewed. Moreover investors would prefer positive skewness and try to reduce kurtosis of their portfolio returns. Therefore the mean variance model (assuming either normally distributed returns or quadratic utility functions) might be too simplifying. The inclusion of higher order moments has therefore been proposed as a possible augmentation of the classical model in order to make it more widely applicable. The resulting problem is non-convex, large scale, and highly relevant in financial optimization. We discuss the solution of the model using two stochastic algorithms. The first algorithm is Differential Evolution (DE). DE is a population based metaheuristic originally designed for continuous optimization problems. New solutions are generated by combining up to four existing solutions plus noise, and acceptance is based on evolutionary principles. The second algorithm is based on the asymptotic behavior of a suitably defined Stochastic Differential Equation (SDE). The SDE consists of three terms. The first term tries to reduce the value of the objective function, the second enforces feasibility of the iterates, while the third adds noise in order to enable the trajectory to climb hills.     

Conditionally heteroscedastic factorial HMMs for time series in finance

In this article, we develop a new approach within the framework of asset pricing models that incorporates two key features of the latent volatility: co‐movement among conditionally heteroscedastic financial returns and switching between different unobservable regimes. By combining latent factor models with hidden Markov chain models we derive a dynamical local model for segmentation and prediction of multivariate conditionally heteroscedastic financial time series. We concentrate more precisely on situations where the factor variances are modelled by univariate generalized quadratic autoregressive conditionally heteroscedastic processes. The expectation maximization algorithm that we have developed for the maximum likelihood estimation is based on a quasi‐optimal switching Kalman filter approach combined with a generalized pseudo‐Bayesian approximation, which yield inferences about the unobservable path of the common factors, their variances and the latent variable of the state process. Extensive Monte Carlo simulations and preliminary experiments obtained with daily foreign exchange rate returns of eight currencies show promising results. Copyright © 2007 John Wiley & Sons, Ltd.     

具有舍入误差微观结构噪音高频数据的杠杆效应分析

本杠杆效应反映了股票收益率与其波动率变动之间的负相关关系,它一直是金融研究的核心问题.在高频时间序列数据中,传统的简单相关系数估计是不相合的,为此一些学者给出了新的杠杆效应刻画-积分杠杆效应,并给出该杠杆效应的估计量.众所周知,高频数据易受市场微观结构噪音的干扰,其中舍入误差是非常重要、实际中普遍存在的一类.高频数据被...     

Robust asset allocation with conditional value at risk using the forward search

The well‐known Markowitz approach to portfolio allocation, based on expected returns and their covariance, seems to provide questionable results in financial management. One motivation for the pitfall is that financial returns have heavier than Gaussian tails, so the covariance of returns, used in the Markowitz model as a measure of portfolio risk, is likely to provide a loose quantification of the effective risk. Additionally, the Markowitz approach is very sensitive to small changes in either the expected returns or their correlation, often leading to irrelevant portfolio allocations. More recent allocation techniques are based on alternative risk measures, such as value at risk (VaR) and conditional VaR (CVaR), which are believed to be more accurate measures of risk for fat‐tailed distributions. Nevertheless, both VaR and CVaR estimates can be influenced by the presence of extreme returns. In this paper, we discuss sensitivity to the presence of extreme returns and outliers when optimizing the allocation, under the constraint of keeping CVaR to a minimum. A robust and efficient approach, based on the forward search, is suggested. A Monte Carlo simulation study shows the advantages of the proposed approach, which outperforms both robust and nonrobust alternatives under a variety of specifications. The performance of the method is also thoroughly evaluated with an application to a set of US stocks.     

Quantile regression for right-censored and length-biased data

Length-biased data arise in many important fields, including epidemiological cohort studies, cancer screening trials and labor economics. Analysis of such data has attracted much attention in the literature. In this paper we propose a quantile regression approach for analyzing right-censored and length-biased data. We derive an inverse probability weighted estimating equation corresponding to the quantile regression to correct the bias due to length-bias sampling and informative censoring. This method can easily handle informative censoring induced by length-biased sampling. This is an appealing feature of our proposed method since it is generally difficult to obtain unbiased estimates of risk factors in the presence of length-bias and informative censoring. We establish the consistency and asymptotic distribution of the proposed estimator using empirical process techniques. A resampling method is adopted to estimate the variance of the estimator. We conduct simulation studies to evaluate its finite sample performance and use a real data set to illustrate the application of the proposed method.     

Using investment portfolio return to combine forecasts: A multiobjective approach

This study investigates the usefulness and efficacy of a multiobjective decision method for financial trading guided by a set of seemingly diverse analysts' forecasts. The paper proposes a goal programming (GP) approach which combines various forecasts based on the performance of their previous investment returns. In our experiment, several series of financial analysts' forecasts are generated by different forecasting techniques. Investment returns on each series of forecasts are measured and then evaluated by three performance criteria, namely, mean, variance, and skewness. Subsequently, these distributional properties of the returns are used to construct a GP model. Results of the GP model provide a set of weights to compose an investment portfolio using various forecasts. To examine its practicality, the approach is tested on several major stock market indices. The performance of the proposed GP approach is compared with those of individual forecasting techniques and a number of forecast combination models suggested by previous studies. This comparison is conducted with respect to different levels of investor preference over return, variance, and skewness. Statistical significance of the results are accessed by bootstrap re-sampling. Empirical results indicate that, for all examined investor preference functions and market indices, the GP approach is significantly better than all other models tested in this study.     

Portfolio selection under DEA-based relative financial strength indicators: case of US industries

Fundamental analysis is an approach for evaluating a firm for its investment-worthiness whereby the firm's financial statements are subject to detailed investigation to predict future stock price performance. In this paper, we propose an approach to combine financial statement data using Data Envelopment Analysis to determine a relative financial strength (RFS) indicator. Such an indicator captures a firm's fundamental strength or competitiveness in comparison to all other firms in the industry/market segment. By analysing the correlation of the RFS indicator with the historical stock price returns within the industry, a well-informed assessment can be made about considering the firm in an equity portfolio. We test the proposed indicator with firms from the technology sector, using various US industries and report correlation analyses. Our preliminary computations using RFS indicator-based stock selection within mean–variance portfolio optimization demonstrate the validity of the proposed approach.     

Modeling financial asset returns with shot noise processes

We introduce a new class of continuous time processes for modeling the rate of returns of financial assets. The statistical characterization is based on the so-called shot noise processes. The probabilistic structure of the shot noise process provides a very realistic framework for asset returns modeling of the stock price processes. Our class of processes exhibits the natural phenomena well known in empirical financial studies:

1. (a) fat-tail distribution function for the asset returns,

2. (b) dependence of the returns,

3. (c) nonstationarity in time.

Financial asset returns in new emerging markets such as those of Eastern European countries exhibit a highly volatile behavior. Statistical investigations of the unconditional distribution of returns of stocks, commodities, exchange rates, etc., show extremely heavy tails and steep peaks around the expectation. We use a class of shot noise processes with Poissonian times and Brownian magnitudes for modeling this phenomenon.     

Fractal Activity Time Models for Risky Asset with Dependence and Generalized Hyperbolic Distributions

Risky asset models with the dependence through fractal activity time are described. The construction of the fractal activity time is implemented via superpositions of Ornstein-Uhlenbeck type processes driven by Lévy noise. The model features both tractable dependence structure and desired marginal distributions of the returns from the generalized hyperbolic class: the Variance Gamma and normal inverse Gaussian. These distributions provide good fit to real financial data. Pricing formulae for the proposed models are derived.     

One‐way analysis of variance with long memory errors and its application to stock return data

Recent empirical results indicate that many financial time series, including stock volatilities, often have long‐range dependencies. Comparing volatilities in stock returns is a crucial part of the risk management of stock investing. This paper proposes two test statistics for testing the equality of mean volatilities of stock returns using the analysis of variance (ANOVA) model with long memory errors. They are modified versions of the ordinary F statistic used in the ANOVA models with independently and identically distributed errors. One has a form of the ordinary F statistic multiplied by a correction factor, which reflects slowly decaying autocorrelations, that is, long‐range dependence. The other is a test statistic such that the degrees of freedom of the denominator in the ordinary F test statistic is calibrated by the so‐called effective sample size. Empirical sizes and powers of the proposed test statistics are examined via Monte Carlo simulation. An application to German stock returns is presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Portfolio adjusting optimization with added assets and transaction costs based on credibility measures

In response to changeful financial markets and investor’s capital, we discuss a portfolio adjusting problem with additional risk assets and a riskless asset based on credibility theory. We propose two credibilistic mean–variance portfolio adjusting models with general fuzzy returns, which take lending, borrowing, transaction cost, additional risk assets and capital into consideration in portfolio adjusting process. We present crisp forms of the models when the returns of risk assets are some deterministic fuzzy variables such as trapezoidal, triangular and interval types. We also employ a quadratic programming solution algorithm for obtaining optimal adjusting strategy. The comparisons of numeral results from different models illustrate the efficiency of the proposed models and the algorithm.     

Portfolio adjusting optimization with added assets and transaction costs based on credibility measures

In response to changeful financial markets and investor’s capital, we discuss a portfolio adjusting problem with additional risk assets and a riskless asset based on credibility theory. We propose two credibilistic mean–variance portfolio adjusting models with general fuzzy returns, which take lending, borrowing, transaction cost, additional risk assets and capital into consideration in portfolio adjusting process. We present crisp forms of the models when the returns of risk assets are some deterministic fuzzy variables such as trapezoidal, triangular and interval types. We also employ a quadratic programming solution algorithm for obtaining optimal adjusting strategy. The comparisons of numeral results from different models illustrate the efficiency of the proposed models and the algorithm.     

Modular solvers for image restoration problems using the discrepancy principle

Many problems in image restoration can be formulated as either an unconstrained non‐linear minimization problem, usually with a Tikhonov‐like regularization, where the regularization parameter has to be determined; or as a fully constrained problem, where an estimate of the noise level, either the variance or the signal‐to‐noise ratio, is available. The formulations are mathematically equivalent. However, in practice, it is much easier to develop algorithms for the unconstrained problem, and not always obvious how to adapt such methods to solve the corresponding constrained problem. In this paper, we present a new method which can make use of any existing convergent method for the unconstrained problem to solve the constrained one. The new method is based on a Newton iteration applied to an extended system of non‐linear equations, which couples the constraint and the regularized problem, but it does not require knowledge of the Jacobian of the irregularity functional. The existing solver is only used as a black box solver, which for a fixed regularization parameter returns an improved solution to the unconstrained minimization problem given an initial guess. The new modular solver enables us to easily solve the constrained image restoration problem; the solver automatically identifies the regularization parameter, during the iterative solution process. We present some numerical results. The results indicate that even in the worst case the constrained solver requires only about twice as much work as the unconstrained one, and in some instances the constrained solver can be even faster. Copyright © 2002 John Wiley & Sons, Ltd.     

基于潜伏因子模型分析的新兴市场国家金融传染效应研究

构建了基于资本资产定价模型为基础的潜伏因子模型对金融危机传染效应进行分析,将引起市场收益率波动的因素分解为"共同因子","特质因子"和"传染因子",同时采用迭代累计平方和算法内生性地对金融危机演化的不同阶段进行了时间上的划分.以2008年全球金融危机期间4个主要新兴市场国家的股票市场为对象进行了实证研究,结果表明这些国家均遭受到了不同程度的传染,其中中国和巴西受到的传染较弱,而印度和俄罗斯受到的传染较强.     

Closed‐form approximations for spread options in Lévy markets

We provide new closed‐form approximations for the pricing of spread options in three specific instances of exponential Lévy markets, ie, when log‐returns are modeled as Brownian motions (Black‐Scholes model), variance gamma processes (VG model), or normal inverse Gaussian processes (NIG model). For the specific case of exchange options (spread options with zero strike), we generalize the well‐known Margrabe formula (1978) that is valid in a Black‐Scholes model to the VG model under a homogeneity assumption.     

Limit theorems for the pre-averaged Hayashi–Yoshida estimator with random sampling

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which possibly depends on the time and the latent diffusion processes, while the sampling times also possibly depend on the observed processes. In a high-frequency setting, we consider a modified version of the pre-averaged Hayashi–Yoshida estimator, and we show that such a kind of estimator has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence.     

Simulation and evaluation of the distribution of interest rate risk

We study methods to simulate term structures in order to measure interest rate risk more accurately. We use principal component analysis of term structure innovations to identify risk factors and we model their univariate distribution using GARCH-models with Student’s t-distributions in order to handle heteroscedasticity and fat tails. We find that the Student’s t-copula is most suitable to model co-dependence of these univariate risk factors. We aim to develop a model that provides low ex-ante risk measures, while having accurate representations of the ex-post realized risk. By utilizing a more accurate term structure estimation method, our proposed model is less sensitive to measurement noise compared to traditional models. We perform an out-of-sample test for the U.S. market between 2002 and 2017 by valuing a portfolio consisting of interest rate derivatives. We find that ex-ante Value at Risk measurements can be substantially reduced for all confidence levels above 95%, compared to the traditional models. We find that that the realized portfolio tail losses accurately conform to the ex-ante measurement for daily returns, while traditional methods overestimate, or in some cases even underestimate the risk ex-post. Due to noise inherent in the term structure measurements, we find that all models overestimate the risk for 10-day and quarterly returns, but that our proposed model provides the by far lowest Value at Risk measures.

     

Forest management optimisation models and habitat diversity: a goal programming approach

This paper proposes an analytical framework, based upon Goal Programming, to incorporate an operational measure of habitat diversity into a forest management optimisation model. First of all, the trade-off curve between the proposed measure of habitat diversity and financial returns is determined. Then, the measure of habitat diversity is integrated in conjunction with other relevant criteria into a compact forest management model. The way in which both models work is explained with the help of a simple but illustrative case study.     

Tracking error decision rules and accumulated wealth

There is compelling evidence that typical decision‐makers, including individual investors and even professional money managers, care about the difference between their portfolio returns and a reference point, or benchmark return. In the context of financial markets, likely benchmarks against which investors compare their own returns include easy‐to‐focus‐on numbers such as one's own past payoffs, historical average payoffs, and the payoffs of competitors. Referring to the gap between one's current portfolio return and the benchmark return as ‘tracking error’, this paper develops a simple model to study the consequences and possible origins of investors who use expected tracking error to guide their portfolio decisions, referred to as ‘tracking error types’. In particular, this paper analyses the level of risk‐taking and accumulated wealth of tracking error types using standard mean‐variance investors as a comparison group. The behaviour of these two types are studied first in isolation, and then in an equilibrium model. Simple analytic results together with statistics summarizing simulated wealth accumulations point to the conclusion that tracking error—whether it is interpreted as reflecting inertia, habituation, or a propensity to make social comparisons in evaluating one's own performance—leads to greater risk‐taking and greater shares of accumulated wealth. This result holds even though the two types are calibrated to be identically risk‐averse when expected tracking error equals zero. In the equilibrium model, increased aggregate levels of risk‐taking reduce the returns on risk. Therefore, the net social effect of tracking‐error‐induced risk‐taking is potentially ambiguous. This paper shows, however, that tracking error promotes a pattern of specialization that helps the economy move towards the path of maximum accumulated wealth.