Gaussian Estimation and Forecasting of Multi-Factor Term Structure Models with an Application to Japan and the United Kingdom

In this paper we extend the exact discrete model of Bergstrom (1966) first used in empirical finance by Brennan and Schwartz (1979) to estimate their two-factor term structure model to estimate other two-factor term structure models using the recent assumption in Nowman (1997) for single factor models. Following Nowman (1997) we use the exact Gaussian estimation methods of Bergstrom (1983–1986, 1990) to estimate two-factor CKLS, Vasicek and CIR models. We estimate the models using monthly UK and Japanese interest rate data and our results indicate that the estimation method works well in practice.     

Gradient-based simulated maximum likelihood estimation for stochastic volatility models using characteristic functions

Parameter estimation and statistical inference are challenging problems for stochastic volatility (SV) models, especially those driven by pure jump Lévy processes. Maximum likelihood estimation (MLE) is usually preferred when a parametric statistical model is correctly specified, but traditional MLE implementation for SV models is computationally infeasible due to high dimensionality of the integral involved. To overcome this difficulty, we propose a gradient-based simulated MLE method under the hidden Markov structure for SV models, which covers those driven by pure jump Lévy processes. Gradient estimation using characteristic functions and sequential Monte Carlo in the simulation of the hidden states are implemented. Numerical experiments illustrate the efficiency of the proposed method.     

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.     

Exact inference and optimal invariant estimation for the stability parameter of symmetric α-stable distributions

Hill estimation (Hill, 1975), the most widespread method for estimating tail thickness of heavy-tailed financial data, suffers from two drawbacks. One is that the optimal number of tail observations to use in the estimation is a function of the unknown tail index being estimated, which diminishes the empirical relevance of the Hill estimation. The other is that the hypothesis test of the underlying data lying in the domain of attraction of an α-stable law (α < 2) or of a normal law (α ≥ 2) for finite samples, is performed on the basis of the asymptotic distribution, which can be different from those for finite samples. In this paper, using the Monte Carlo technique, we propose an exact test method for the stability parameter of α-stable distributions which is based on the Hill estimator, yet is able to provide exact confidence intervals for finite samples. Our exact test method automatically includes an estimation procedure which does not need the assumption of a known number of observations on the distributional tail. Empirical applications demonstrate the advantages of our new method in comparison with the Hill estimation.     

Understanding analysts forecasts

The purpose of this paper is to model analysts’ forecasts. The paper differs from the previous research in that we do not focus on how accurate these predictions may be. Accuracy may indeed be an important quality but we argue instead that another equally important aspect of the analysts’ job is to predict and describe the impact of jump events. In effect, the analysts’ role is one of scenario prediction. Using a Bayesian-inspired generalised method of moments estimation procedure, we use this notion of scenario prediction combined with the structure of the Morgan Stanley analysts’ forecasting database to model normal (base), optimistic (bull) and pessimistic (bear) forecast scenarios for a set of reports from Asia (excluding Japan) for 2007–2008. Since the estimation procedure is unique to this paper, a rigorous derivation of the asymptotic properties of the resulting estimator is also provided.     

Parameter estimation risk in asset pricing and risk management: A Bayesian approach

Parameter estimation risk is non-trivial in both asset pricing and risk management. We adopt a Bayesian estimation paradigm supported by the Markov Chain Monte Carlo inferential techniques to incorporate parameter estimation risk in financial modelling. In option pricing activities, we find that the Merton's Jump-Diffusion (MJD) model outperforms the Black-Scholes (BS) model both in-sample and out-of-sample. In addition, the construction of Bayesian posterior option price distributions under the two well-known models offers a robust view to the influence of parameter estimation risk on option prices as well as other quantities of interest in finance such as probabilities of default. We derive a VaR-type parameter estimation risk measure for option pricing and we show that parameter estimation risk can bring significant impact to Greeks' hedging activities. Regarding the computation of default probabilities, we find that the impact of parameter estimation risk increases with gearing level, and could alter important risk management decisions.     

Fitting prices with a complete model

The aim of this paper is to introduce some methodologies for parameter estimation in Hobson and Rogers stochastic volatility model (1998). We pay a specific attention to the so-called feedback parameter, which is shown to be crucial for the model to fit correctly the smile curve of implied volatility and we introduce different procedures for the estimation of the volatility parameters. We finally test the pricing capability of the model on market options prices on the FTSE100 and the S&P500 Indexes, according to the estimation methodologies introduced.     

Empirical performance of Gaussian affine dynamic term structure models in the presence of autocorrelation misspecification bias

Recently, several authors have documented the presence of estimation bias in Gaussian affine dynamic term structure models (GADTSM). However, only a few applications involving its impact on the empirical performance of GADTSM exist in the extant literature, and these studies focus solely on discrete-time vector autoregressive (VAR) based GADTSM and concentrate on issues of small-sample bias and persistence. In this paper, we provide a comprehensive investigation of this issue that includes the estimation of both discrete-time VAR based GADTSM and continuous-time GADTSM at multiple data frequencies through a unique empirical design and two Monte Carlo simulation experiments, within which we construct estimation bias from the serial correlation in yield pricing errors. Our findings show that, although, empirical performance of all studied GADTSM are severely impacted by estimation bias, discrete-time GADTSM are more severely impacted by estimation bias than continuous-time GADTSM. Building on theoretical arguments developed in previous works, we attribute this finding to the strong dependence of discrete-time VAR based GADTSM on the ordinary least squares econometric technique relative to the continuous-time GADTSM for which general maximum likelihood estimation is more suitable.     

The economic determinants of the market reaction to proposed mandatory accounting changes in the oil and gas industry: A cross-sectional analysis

This paper examines the economic reasons for the observed negative abnormal common stock performance of firms whose reported earnings and stockholders' equity were negatively affected by the proposed elimination of full cost accounting in the oil and gas industry. Four explanations of the market effects of this mandatory accounting change are examined: (1) naive investor theory, (2) modified naive investor theory, (3) contracting cost theory, and (4) estimation risk theory. These hypotheses are developed in detail and used to generate variables for a cross-sectional model which explains observed return behavior. The effect of the accounting change on total stockholder's equity, the existence of financial contracts denominated in terms of accounting numbers and, to a lesser extent, firm size are shown to be important explanatory variables. The importance of these variables is consistent with both the contracting cost and estimation risk theories.     

Socially responsible investment portfolios: Does the optimization process matter?

This study investigates the impact of the choice of optimization technique when constructing Socially Responsible Investment (SRI) portfolios. Corporate Social Performance (CSP) scores are price sensitive information that is subject to considerable estimation risk. Therefore, uncertainty in the input parameters is greater for SRI portfolios than conventional portfolios, and this affects the selection of the appropriate optimization method. We form SRI portfolios based on six different approaches and compare their performance along the dimensions of risk, risk-return trade-off, diversification and stability. Our results for SRI portfolios contradict those of the conventional portfolio optimization literature. We find that the more “formal” optimization approaches (Black-Litterman, Markowitz and robust estimation) lead to SRI portfolios that are both less risky and have superior risk-return trade-offs than do more simplistic approaches; although they also have more unstable asset allocations and lower diversification. Our conclusions are robust to a series of tests, including the use of different estimation windows and stricter screening criteria.     

Operational risk

This paper provides an economic and mathematical characterization of operational risk useful for clarifying the issues related to estimation and the determination of economic capital. The insights for this characterization originate in the corporate finance literature. Operational risk is subdivided into two types, either: (i) the risk of a loss due to the firm’s operating technology, or (ii) the risk of a loss due to agency costs. These two types of operational risks generate loss processes with different economic characteristics. We argue that the current methodology for the determination of economic capital for operational risk is overstated. It is biased high because the computation omits the bank’s net present value (NPV) generating process. We also show that although it is conceptually possible to estimate the operational risk processes’ parameters using only market prices, the non-observability of the firm’s value makes this an unlikely possibility, except in rare cases. Instead, we argue that data internal to the firm, in conjunction with standard hazard rate estimation procedures, provides a more fruitful alternative.     

Gibbs posterior inference on value-at-risk

ABSTRACT

Accurate estimation of value-at-risk (VaR) and assessment of associated uncertainty is crucial for both insurers and regulators, particularly in Europe. Existing approaches link data and VaR indirectly by first linking data to the parameter of a probability model, and then expressing VaR as a function of that parameter. This indirect approach exposes the insurer to model misspecification bias or estimation inefficiency, depending on whether the parameter is finite- or infinite-dimensional. In this paper, we link data and VaR directly via what we call a discrepancy function, and this leads naturally to a Gibbs posterior distribution for VaR that does not suffer from the aforementioned biases and inefficiencies. Asymptotic consistency and root-n concentration rate of the Gibbs posterior are established, and simulations highlight its superior finite-sample performance compared to other approaches.     

Sampling error and double shrinkage estimation of minimum variance portfolios

Shrinkage estimators of the covariance matrix are known to improve the stability over time of the Global Minimum Variance Portfolio (GMVP), as they are less error-prone. However, the improvement over the empirical covariance matrix is not optimal for small values of n, the estimation sample size. For typical asset allocation problems, with n small, this paper aims at proposing a new method to further reduce sampling error by shrinking once again traditional shrinkage estimators of the GMVP. First, we show analytically that the weights of any GMVP can be shrunk – within the framework of the ridge regression – towards the ones of the equally-weighted portfolio in order to reduce sampling error. Second, Monte Carlo simulations and empirical applications show that applying our methodology to the GMVP based on shrinkage estimators of the covariance matrix, leads to more stable portfolio weights, sharp decreases in portfolio turnovers, and often statistically lower (resp. higher) out-of-sample variances (resp. Sharpe ratios). These results illustrate that double shrinkage estimation of the GMVP can be beneficial for realistic small estimation sample sizes.     

GHICA — Risk analysis with GH distributions and independent components

Over recent years, a study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical difficulty. The primary aim of this paper is to present a realistic and fast method, GHICA, which overcomes the limitations in multivariate risk analysis. The idea is to first retrieve independent components (ICs) out of the observed high-dimensional time series and then individually and adaptively fit the resulting ICs in the generalized hyperbolic (GH) distributional framework. For the volatility estimation of each IC, the local exponential smoothing technique is used to achieve the best possible accuracy of estimation. Finally, the fast Fourier transformation technique is used to approximate the density of the portfolio returns.The proposed GHICA method is applicable to covariance estimation as well. It is compared with the dynamic conditional correlation (DCC) method based on the simulated data with d = 50 GH distributed components. We further implement the GHICA method to calculate risk measures given 20-dimensional German DAX portfolios and a dynamic exchange rate portfolio. Several alternative methods are considered as well to compare the accuracy of calculation with the GHICA one.     

Country versus sector factors in equity returns: The roles of non-unit exposures

In this paper we disentangle, analytically and empirically, the roles of the unit-exposure restriction in Heston and Rouwenhorst (1994). We show that if the purpose is to construct factors, the unit-exposure variance-analysis model can be viewed as just an algorithm that does not really assume a return-generating process; and in practice the effect of relaxing the restriction is immaterial. The restriction is more important if one wants to estimate whether, for a typical stock, the country factor generates more variance than the sector factor: exposure estimation becomes more important (i) the further the average exposures are from unity; or (ii) the higher the dispersion of the exposures. With respect to (i), the more important the corrections for sector (or geographical) structure in country (or sector) factors are, the more the average exposure falls below unity. Thus, the average exposure provides an alternative indicator of the importance of country versus sector effects. We empirically find that the average sector exposure is low (0.3) compared to the average country exposure (0.9). With respect to (ii) we correct the dispersion of exposures for estimation error in the exposures. We find that in our sample these estimation error corrections are more important for sector factors than for country factors, and that country factors are generating far more variance, in a typical stock's return, than do sector factors.     

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.     

A faster estimation method for the probability of informed trading using hierarchical agglomerative clustering

The probability of informed trading (PIN) is a commonly used market microstructure measure for detecting the level of information asymmetry. Estimating PIN can be problematic due to corner solutions, local maxima and floating point exceptions (FPE). Yan and Zhang [J. Bank. Finance, 2012, 36, 454–467] show that whilst factorization can solve FPE, boundary solutions appear frequently in maximum likelihood estimation for PIN. A grid search initial value algorithm is suggested to overcome this problem. We present a faster method for reducing the likelihood of boundary solutions and local maxima based on hierarchical agglomerative clustering (HAC). We show that HAC can be used to determine an accurate and fast starting value approximation for PIN. This assists the maximum likelihood estimation process in both speed and accuracy.     

Systematic risk estimation in the presence of large and many outliers

It is well recognized that the effect of extreme points on systematic risk estimates is not adequately captured through least squares estimation. This article uses the reweighted least median squares (RWLMS) approach, first proposed by Rousseeuw (1984), which accurately detects outlier presence. Using a large sample of 1350 NYSE/AMEX firms, the article demonstrates that least squares does indeed mask several potentially influential points, that this masking is very pervasive over the sample, and that it may persist even after conventional robust estimation techniques are applied. When these masked points are “unmasked” by RWLMS and zero weights assigned to such observations, the resulting RWLMS estimates of beta are on average 10%–15% smaller. However, a Bayesian treatment of such points (assigning a priori nonzero weights) is possible in both one and two factor market models.     

Evidence on using the estimation of level 3 fair values as an earnings management tool: evidence from Taiwan

This study aims to present direct evidence on whether the estimations of Level 3 fair values (L3FVs) are used as an earnings management tool. Researchers argue this possibility but there is a lack of direct evidence. Moreover, this study tests the moderating effect of managerial education level on using the estimation of L3FVs as an earnings management tool. The results show that the firms suspected of earnings management report relatively large abnormal valuation adjustments to L3FVs, suggesting that the estimations of L3FVs are used as an earnings management tool. Furthermore, the results indicate that the graduate education of accounting and financial managers in finance reduces the use of the estimation of L3FVs to manage earnings.