Two-step estimation of the volatility functions in diffusion models with empirical applications

In this article, we develop a two-step estimation procedure for the volatility function in diffusion models. We firstly estimate the volatility series at sampling time points based on high-frequency data. Then, the volatility function estimator can be obtained by using the kernel smoothing method. The resulting estimators are presented based on high-frequency data, and are shown to be consistent and asymptotically normal. We also consider boundary issues and then propose two methods to handle them. The asymptotic normality of two boundary-corrected estimators is established under some suitable conditions. The proposed estimators are illustrated by Monte Carlo simulations and real data.     

Nonparametric methods with applications to hedonic models

Current real estate statistical valuation involves the estimation of parameters within a posited specification. Suchparametric estimation requires judgment concerning model (1) variables; and (2) functional form. In contrast,nonparametric regression estimation requires attention to (1) but permits greatly reduced attention to (2). Parametric estimators functionally model the parameters and variables affectingE(y¦x) while nonparametric estimators directly modelpdf(y, x) and henceE(y¦x).This article applies the kernel nonparametric regression estimator to two different data sets and specifications. The article shows the nonparametric estimator outperforms the standard parametric estimator (OLS) across variable transformations and across data subsets differing in quality. In addition, the article reviews properties of nonparametric estimators, presents the history of nonparametric estimators in real estate, and discusses a representation of the kernel estimator as a nonparametric grid method.     

Finite sample accuracy and choice of sampling frequency in integrated volatility estimation

We consider the properties of three estimation methods for integrated volatility, i.e. realized volatility, Fourier, and wavelet estimation, when a typical sample of high-frequency data is observed. We employ several different generating mechanisms for the instantaneous volatility process, e.g. Ornstein–Uhlenbeck, long memory, and jump processes. The possibility of market microstructure contamination is also entertained using models with bid-ask bounce and price discreteness, in which case alternative estimators with theoretical justification under market microstructure noise are also examined. The estimation methods are compared in a simulation study which reveals a general robustness towards persistence or jumps in the latent stochastic volatility process. However, bid-ask bounce effects render realized volatility and especially the wavelet estimator less useful in practice, whereas the Fourier method remains useful and is superior to the other two estimators in that case. More strikingly, even compared to bias correction methods for microstructure noise, the Fourier method is superior with respect to RMSE while having only slightly higher bias. A brief empirical illustration with high-frequency GE data is also included.     

Parametric,semiparametric, and nonparametric estimation of characteristic values within mass assessment and hedonic pricing models

Parametric estimators, such as OLS, attain high efficiency for well-specified models. Nonparametric estimators greatly reduce specification error but at the cost of efficiency. Semiparametric estimators compromise between these dual goals of efficiency and specification error. Semiparametric estimators can assume general forms within classes of functional forms. This paper applies OLS, the kernel nonparametric regression estimator, and the semi-parametric estimator of Powell, Stock, and Stoker (1989) to a data set, which should, based on theory and previous empirical work, yield positive coefficients. The semiparametric estimator, on average, displayed the performance most consistent with prior expectations followed by the nonparametric and parametric estimators. In addition, the paper shows how the semiparametric estimator can provide insights into the form of misspecification and suggest data transformations.     

Measuring tail thickness under GARCH and an application to extreme exchange rate changes

Accurate modeling of extreme price changes is vital to financial risk management. We examine the small sample properties of adaptive tail index estimators under the class of student-t marginal distribution functions including generalized autoregressive conditional heteroskedastic (GARCH) models and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias relates to the underlying model and may be positively as well as negatively signed. The empirical study of daily exchange rate changes reveals substantial differences in measured tail thickness due to small sample bias. Thus, high quantile estimation may lead to a substantial underestimation of tail risk.     

Nonparametric realized volatility estimation in the international equity markets

Using high-frequency intraday data, we construct, test and model seven new realized volatility estimators for six international equity indices. We detect jumps in these estimators, construct the jump components of volatility and perform various tests on their properties. Then we use the class of heterogeneous autoregressive (HAR) models for assessing the relevant effects of jumps on volatility. Our results expand and complement the previous literature on the nonparametric realized volatility estimation in terms of volatility jumps being examined and modeled for the international equity market, using such a variety of new realized volatility estimators. The selection of realized volatility estimator greatly affects jump detection, magnitude and modeling. The properties each volatility estimator tries to incorporate affect the detection, magnitude and properties of jumps. These volatility-estimation and jump properties are also evident in jump modeling based on statistical and economic terms.     

Estimating continuous-time stochastic volatility models of the short-term interest rate: a comparison of the generalized method of moments and the Kalman filter

This paper examines a model of short-term interest rates that incorporates stochastic volatility as an independent latent factor into the popular continuous-time mean-reverting model of Chan et al. (J Financ 47:1209–1227, 1992). I demonstrate that this two-factor specification can be efficiently estimated within a generalized method of moments (GMM) framework using a judicious choice of moment conditions. The GMM procedure is compared to a Kalman filter estimation approach. Empirical estimation is implemented on US Treasury bill yields using both techniques. A Monte Carlo study of the finite sample performance of the estimators shows that GMM produces more heavily biased estimates than does the Kalman filter, and with generally larger mean squared errors.     

The Return Performance of Cubic Market Model: An Application to Emerging Markets

This article studies the performance of the high-order moment capital asset pricing model (CAPM) market models in emerging markets. We apply the cubic market model (4-moment CAPM) to 16 emerging market stock indices ranging from January 2010 to September 2015. Performance of the model is evaluated through the Fama and MacBeth’s two-step regression and through different corrections proposed in the literature, as well as generalized method of moments (GMM) estimation. According to Fama–MacBeth’s procedure, CAPM, the quadratic and cubic market models seem to be insignificant for the analyzed sample; however, the GMM estimation shows that quadratic model is valid for Indian, Polish, and Thai country indices, whereas cubic market model is accurate for Indian country index.     

The heteroskedasticity-consistent covariance estimator in accounting

The main purpose of this paper is to compare the White (1980) heteroskedasticity-consistent (HC) covariance matrix estimator with alternative estimators. Many regression packages compute the White (1980) heteroskedasticity-consistent (HC) covariance matrix estimator. The common procedure in Accounting and Finance research to deal with the heteroskedasticity problem is based on this estimator, despite its worse finite-samples properties when compared with other consistent estimators. In this paper we compare several HC covariance matrix estimators based on a sample of 3706 European listed companies from Austria, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden and the United Kingdom. We conclude that HC standard errors increase when finite-samples more appropriate estimators are considered and in the most part of countries the Ohlson (1995) model coefficients estimates became statistically insignificant. This can be explained by the high leverage points in the design matrix. To the best of our knowledge it is the first time that these alternative estimators are compared with the one of White (1980) in accounting research.     

On the estimation and comparison of short-rate models using the generalised method of moments

Subsequent to the influential paper of [Chan, K.C., Karolyi, G.A., Longstaff, F.A., Sanders, A.B., 1992. An empirical comparison of alternative models of the short-term interest rate. Journal of Finance 47, 1209–1227], the generalised method of moments (GMM) has been a popular technique for estimation and inference relating to continuous-time models of the short-term interest rate. GMM has been widely employed to estimate model parameters and to assess the goodness-of-fit of competing short-rate specifications. The current paper conducts a series of simulation experiments to document the bias and precision of GMM estimates of short-rate parameters, as well as the size and power of [Hansen, L.P., 1982. Large sample properties of generalised method of moments estimators. Econometrica 50, 1029–1054], J-test of over-identifying restrictions. While the J-test appears to have appropriate size and good power in sample sizes commonly encountered in the short-rate literature, GMM estimates of the speed of mean reversion are shown to be severely biased. Consequently, it is dangerous to draw strong conclusions about the strength of mean reversion using GMM. In contrast, the parameter capturing the levels effect, which is important in differentiating between competing short-rate specifications, is estimated with little bias.     

In search of robust methods for dynamic panel data models in empirical corporate finance

We examine which methods are appropriate for estimating dynamic panel data models in empirical corporate finance. Our simulations show that the instrumental variable and GMM estimators are unreliable, and sensitive to the presence of unobserved heterogeneity, residual serial correlation, and changes in control parameters. The bias-corrected fixed-effects estimators, based on an analytical, bootstrap, or indirect inference approach, are found to be the most appropriate and robust methods. These estimators perform reasonably well even in models with fractional dependent variables censored at [0, 1]. We verify these results in two empirical applications, on dynamic capital structure and cash holdings.     

Zero-intelligence realized variance estimation

Given a time series of intra-day tick-by-tick price data, how can realized variance be estimated? The obvious estimator—the sum of squared returns between trades—is biased by microstructure effects such as bid–ask bounce and so in the past, practitioners were advised to drop most of the data and sample at most every five minutes or so. Recently, however, numerous alternative estimators have been developed that make more efficient use of the available data and improve substantially over those based on sparsely sampled returns. Yet, from a practical viewpoint, the choice of which particular estimator to use is not a trivial one because the study of their relative merits has primarily focused on the speed of convergence to their asymptotic distributions, which in itself is not necessarily a reliable guide to finite sample performance (especially when the assumptions on the price or noise process are violated). In this paper we compare a comprehensive set of nineteen realized variance estimators using simulated data from an artificial “zero-intelligence” market that has been shown to mimic some key properties of actual markets. In evaluating the competing estimators, we concentrate on efficiency but also pay attention to implementation, practicality, and robustness. One of our key findings is that for scenarios frequently encountered in practice, the best variance estimator is not always the one suggested by theory. In fact, an ad hoc implementation of a subsampling estimator, realized kernel, or maximum likelihood realized variance, delivers the best overall result. We make firm practical recommendations on choosing and implementing a realized variance estimator, as well as data sampling.     

Endogeneity and the dynamics of internal corporate governance

We use a well-developed dynamic panel generalized method of moments (GMM) estimator to alleviate endogeneity concerns in two aspects of corporate governance research: the effect of board structure on firm performance and the determinants of board structure. The estimator incorporates the dynamic nature of internal governance choices to provide valid and powerful instruments that address unobserved heterogeneity and simultaneity. We re-examine the relation between board structure and performance using the GMM estimator in a panel of 6,000 firms over a period from 1991 to 2003, and find no causal relation between board structure and current firm performance. We illustrate why other commonly used estimators that ignore the dynamic relationship between current governance and past firm performance may be biased. We discuss where it may be appropriate to consider the dynamic panel GMM estimator in corporate governance research, as well as caveats to its use.     

Empirical Bayes credibility

Abstract

A credibility estimator is Bayes in the restricted class of linear estimators and may be viewed as a linear approximation to the (unrestricted) Bayes estimator. When the structural parameters occurring in a credibility formula are replaced by consistent estimators based on data from a collective of similar risks,we obtain an empirical credibility estimator, which is a credibility counterpart of empirical Bayes estimators. Empirical credibility estimators are proposed under various model assumptions, and sufficient conditions for asymptotic optimality are established.     

Skills, Schooling, and Household Income in Ghana

This article examines the impact of cognitive skills on theincome of households in Ghana. It uses scores on mathematicsand English tests to measure cognitive skills and estimatesthe returns to these skills based on farm profit, off-farm income,and total income. The article uses Powell's censored least absolutedeviations and symmetrically trimmed least squares estimatorsto estimate farm and off-farm income. In contrast to Heckman'stwo-step or the Tobit estimator, Powell's estimators are consistentin the presence of heteroscedasticity and are robust to otherviolations of normality. The results show that cognitive skillshave a positive effect on total and off-farm income but do nothave a statistically significant effect on farm income.     

Estimating cost of capital in firm valuations with arithmetic or geometric mean – or better use the Cooper estimator?

We test the extent and determinants of bias effects of the arithmetic as well as the geometric mean estimator and the estimator of Cooper [1996. Arithmetic versus geometric mean estimators: Setting discount rates for capital budgeting. European Financial Management 2 (July): 157–67] regarding discount rate estimation for firm valuation by way of a bootstrap approach for 13 different countries. The Cooper estimator is superior to both the geometric and the (conventional) arithmetic mean estimator. However, a ‘truncated’ version of the arithmetic mean estimator leads generally to better estimation outcomes than the Cooper estimator. This means that, in order to reduce problems of upward-biased firm value estimates, expected cash flows beyond a certain time horizon are completely neglected in terminal value estimation. Such an approach seems particularly reasonable for the valuation of young growth companies as well as for companies from quickly developing countries such as Brazil, China, or Thailand, because the bias in terminal value estimation is increasing in the growth rate of future expected cash flows.     

The accuracy of real estate indices: Repeat sale estimators

Simulation techniques allow us to examine the behavior and accuracy of several repeat sales regression estimators used to construct real estate return indices. We show that the generalized least squares (GLS) method is the maximum likelihood estimator, and we show how estimation accuracy can be significantly improved through a Baysian approach. In addition, we introduce a biased estimation procedure based upon the James and Stein method to address the problems of multicollinearity common to the procedure.     

Machine learning for quantitative finance: fast derivative pricing,hedging and fitting

In this paper, we show how we can deploy machine learning techniques in the context of traditional quant problems. We illustrate that for many classical problems, we can arrive at speed-ups of several orders of magnitude by deploying machine learning techniques based on Gaussian process regression. The price we have to pay for this extra speed is some loss of accuracy. However, we show that this reduced accuracy is often well within reasonable limits and hence very acceptable from a practical point of view. The concrete examples concern fitting and estimation. In the fitting context, we fit sophisticated Greek profiles and summarize implied volatility surfaces. In the estimation context, we reduce computation times for the calculation of vanilla option values under advanced models, the pricing of American options and the pricing of exotic options under models beyond the Black–Scholes setting.     

Non-parametric estimation of historical volatility

Evolving volatility is a dominant feature observed in most financial time series and a key parameter used in option pricing and many other financial risk analyses. A number of methods for non-parametric scale estimation are reviewed and assessed with regard to the stylized features of financial time series. A new non-parametric procedure for estimating historical volatility is proposed based on local maximum likelihood estimation for the t-distribution. The performance of this procedure is assessed using simulated and real price data and is found to be the best among estimators we consider. We propose that it replaces the moving variance historical volatility estimator.     

Aggregation of Nonparametric Estimators for Volatility Matrix

An aggregated method of nonparametric estimators based on time-domainand state-domain estimators is proposed and studied. To attenuatethe curse of dimensionality, we propose a factor modeling strategy.We first investigate the asymptotic behavior of nonparametricestimators of the volatility matrix in the time domain and inthe state domain. Asymptotic normality is separately establishedfor nonparametric estimators in the time domain and state domain.These two estimators are asymptotically independent. Hence,they can be combined, through a dynamic weighting scheme, toimprove the efficiency of volatility matrix estimation. Theoptimal dynamic weights are derived, and it is shown that theaggregated estimator uniformly dominates volatility matrix estimatorsusing time-domain or state-domain smoothing alone. A simulationstudy, based on an essentially affine model for the term structure,is conducted, and it demonstrates convincingly that the newlyproposed procedure outperforms both time- and state-domain estimators.Empirical studies further endorse the advantages of our aggregatedmethod.