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.     

Nonparametric Estimation of Expected Shortfall

The expected shortfall is an increasingly popular risk measurein financial risk management and it possesses the desired sub-additivityproperty, which is lacking for the value at risk (VaR). We considertwo nonparametric expected shortfall estimators for dependentfinancial losses. One is a sample average of excessive losseslarger than a VaR. The other is a kernel smoothed version ofthe first estimator (Scaillet, 2004 Mathematical Finance), hopingthat more accurate estimation can be achieved by smoothing.Our analysis reveals that the extra kernel smoothing does notproduce more accurate estimation of the shortfall. This is differentfrom the estimation of the VaR where smoothing has been shownto produce reduction in both the variance and the mean squareerror of estimation. Therefore, the simpler ES estimator basedon the sample average of excessive losses is attractive forthe shortfall estimation.     

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.     

Value at risk estimation by quantile regression and kernel estimator

Risk management has attracted a great deal of attention, and Value at Risk (VaR) has emerged as a particularly popular and important measure for detecting the market risk of financial assets. The quantile regression method can generate VaR estimates without distributional assumptions; however, empirical evidence has shown the approach to be ineffective at evaluating the real level of downside risk in out-of-sample examination. This paper proposes a process in VaR estimation with methods of quantile regression and kernel estimator which applies the nonparametric technique with extreme quantile forecasts to realize a tail distribution and locate the VaR estimates. Empirical application of worldwide stock indices with 29 years of data is conducted and confirms the proposed approach outperforms others and provides highly reliable estimates.     

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.     

On the way to recovery: A nonparametric bias free estimation of recovery rate densities

In this paper we analyse recovery rates on defaulted bonds using the Standard & Poor's/PMD database for the years 1981–1999. Due to the specific nature of the data (observations lie within 0 and 1), we must rely on nonstandard econometric techniques. The recovery rate density is estimated nonparametrically using a beta kernel method. This method is free of boundary bias, and Monte Carlo comparison with competing nonparametric estimators show that the beta kernel density estimator is particularly well suited for density estimation on the unit interval. We challenge the usual market practice to model parametrically recovery rates using a beta distribution calibrated on the empirical mean and variance. This assumption is unable to replicate multimodal distributions or concentration of data at total recovery and total loss. We evaluate the impact of choosing the beta distribution on the estimation of credit Value-at-Risk.     

Nonparametric Inference of Value-at-Risk for Dependent Financial Returns

The article considers nonparametric estimation of value-at-risk(VaR) and associated standard error estimation for dependentfinancial returns. Theoretical properties of the kernel VaRestimator are investigated in the context of dependence. Thepresence of dependence affects the variance of the VaR estimatesand has to be taken into consideration in order to obtain adequateassessment of their variation. An estimation procedure of thestandard errors is proposed based on kernel estimation of thespectral density of a derived series. The performance of theVaR estimators and the proposed standard error estimation procedureare evaluated by theoretical investigation, simulation of commonlyused models for financial returns, and empirical studies onreal financial return series.     

Multivariate Boundary Kernels from Local Linear Estimation

Lejeune and Sarda (1992) and Jones (1993) introduced the principle of local linear estimation to nonparametric estimation of smooth densities on the positive real axes. This methodology results in the basic kernel smoother with Gasser and Müller (1979) type boundary kernels when estimating close to a boundary. This principle is extended to nonparametric multivariate density estimation with arbitrary boundary regions.     

Mortgage Default: Classification Trees Analysis

We apply the powerful, flexible, and computationally efficient nonparametric Classification and Regression Trees (CART) algorithm to analyze real estate mortgage data. CART is particularly appropriate for our data set because of its strengths in dealing with large data sets, high dimensionality, mixed data types, missing data, different relationships between variables in different parts of the measurement space, and outliers. Moreover, CART is intuitive and easy to interpret and implement. We discuss the pros and cons of CART in relation to traditional methods such as linear logistic regression, nonparametric additive logistic regression, discriminant analysis, partial least squares classification, and neural networks, with particular emphasis on real estate. We use CART to produce the first academic study of Israeli mortgage default data. We find that borrowers features, rather than mortgage contract features, are the strongest predictors of default if accepting icbadli borrowers is more costly than rejecting good ones. If the costs are equal, mortgage features are used as well. The higher (lower) the ratio of misclassification costs of bad risks versus good ones, the lower (higher) are the resulting misclassification rates of bad risks and the higher (lower) are the misclassification rates of good ones. This is consistent with real-world rejection of good risks in an attempt to avoid bad ones.     

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.     

On a nonparametric estimator for ruin probability in the classical risk model

In this paper, we present a nonparametric estimator for ruin probability in the classical risk model with unknown claim size distribution. We construct the estimator by Fourier inversion and kernel density estimation method. Under some conditions imposed on the kernel, bandwidth and claim size density, we present some large sample properties of the estimator. Some simulation studies are also given to show the finite sample performance of the estimator.     

Alternative constructions of Tobin's q: An empirical comparison

Although Tobin's q is an attractive theoretical firm performance measure, its empirical construction is subject to considerable measurement error. In this paper we compare five estimators of q that range from a simple-to-construct estimator based on book-values to a relatively complex estimator based upon the methodology developed by Lindenberg and Ross (1981). We present comparisons of the means, medians and variances of the q estimates, and examine how robust sorting and regression results are to changes in the construction of q. We find that empirical results are sensitive to the method used to estimate Tobin's q. The simple-to-construct estimator produces empirical results that differ significantly from the alternative estimators. Among the other four estimators, one developed by Hall (1990) produces means that are higher and variances that are larger than the three alternative estimators, but does approximate those estimators in most of the empirical comparisons. Those three alternative q ratio estimators, furthermore, produce empirical results that are robust.     

Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution

Abstract

Estimation of the tail index parameter of a single-parameter Pareto model has wide application in actuarial and other sciences. Here we examine various estimators from the standpoint of two competing criteria: efficiency and robustness against upper outliers. With the maximum likelihood estimator (MLE) being efficient but nonrobust, we desire alternative estimators that retain a relatively high degree of efficiency while also being adequately robust. A new generalized median type estimator is introduced and compared with the MLE and several well-established estimators associated with the methods of moments, trimming, least squares, quantiles, and percentile matching. The method of moments and least squares estimators are found to be relatively deficient with respect to both criteria and should become disfavored, while the trimmed mean and generalized median estimators tend to dominate the other competitors. The generalized median type performs best overall. These findings provide a basis for revision and updating of prevailing viewpoints. Other topics discussed are applications to robust estimation of upper quantiles, tail probabilities, and actuarial quantities, such as stop-loss and excess-of-loss reinsurance premiums that arise concerning solvency of portfolios. Robust parametric methods are compared with empirical nonparametric methods, which are typically nonrobust.     

Relative performance of the grid, nearest neighbor, and OLS estimators

This article provides various paradigms for the grid estimator, the most useful being a representation of the grid estimator as a combination of the nonparametric nearest neighbor estimator and a parametric estimator. Hence, the grid estimator falls into the class of semiparametric estimators. The article used this representation to derive the relative efficiency of the nearest neighbor, grid, and OLS estimators. Under statistically perfect conditions, the OLS estimator dominated the grid estimator, which in turn dominated the nearest neighbor estimator. A Monte Carlo experiment verified the theoretical results. A second Monte Carlo experiment showed the fragility of the OLS superiority to misspecification. The results cast light upon appraisal practice.     

Spillovers in risk of financial institutions

ABSTRACT

We analyse the total and directional spillovers across a set of financial institution systemic risk state variables: credit risk, real estate market risk, interest rate risk, interbank liquidity risk and overall market risk. We examine the response of the spillover levels, within the set of systemic risk state variables, to a number of events in the financial markets and to initiatives undertaken by the European Central Bank and the Bank of England. The relationship between the time-varying spillovers and policy-related events is analysed using a multiple structural break estimation procedure and looking at the temporary increases in the spillover indices. Our sample includes five European Union countries: core countries France and Germany, periphery countries Spain and Italy, and a reference country, the UK. We show that national stock markets and real estate markets have a leading role in shock transmission across selected state variables. However, the role of the other variables reverses over the course of the crisis. We document that the total and net spillover indices react strongly to the events relating to financial assistance packages in Europe.     

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.     

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.     

How Do Institutional Factors Affect International Real Estate Returns?

Prior international real estate studies recognize the importance of country-specific factors for explaining real estate security returns. Using firm level observations from the FTSE NAREIT/EPRA Index for 2004?C2006, we construct a set of multifactor multivariate statistical regression models to identify and pin-point country-specific institutional features that determine differences for excess real estate security returns. Our analyses indicate that the excess real estate returns (i.e., required risk premiums) are, in part, determined by the quality of a country??s legal system and the corporate governance environment, controlling for various country-specific macro-economic variables and firm-level characteristics. We further find that the impact of institutional factors on international real estate returns is more prominent in the Asia-Pacific Region, and recent development of the REIT structure across the world does not alter the importance of corporate governance and legal system quality for determining real estate returns.     

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.     

Valuation in US Commercial Real Estate

We consider a log‐linearized version of a discounted rents model to price commercial real estate as an alternative to traditional hedonic models. First, we verify a key implication of the model, namely, that cap rates forecast commercial real estate returns. We do this using two different methodologies: time series regressions of 21 US metropolitan areas and mixed data sampling (MIDAS) regressions with aggregate REIT returns. Both approaches confirm that the cap rate is related to fluctuations in future returns. We also investigate the provenance of the predictability. Based on the model, we decompose fluctuations in the cap rate into three parts: (i) local state variables (demographic and local economic variables); (ii) growth in rents; and (iii) an orthogonal part. About 30% of the fluctuation in the cap rate is explained by the local state variables and the growth in rents. We use the cap rate decomposition into our predictive regression and find a positive relation between fluctuations in economic conditions and future returns. However, a larger and significant part of the cap rate predictability is due to the orthogonal part, which is unrelated to fundamentals. This implies that economic conditions, which are also used in hedonic pricing of real estate, cannot fully account for future movements in returns. We conclude that commercial real estate prices are better modelled as financial assets and that the discounted rent model might be more suitable than traditional hedonic models, at least at an aggregate level.