Parameterizing credit risk models with rating data

Estimates of average default probabilities for borrowers assigned to each of a financial institution's internal credit risk rating grades are crucial inputs to portfolio credit risk models. Such models are increasingly used in setting financial institution capital structure, in internal control and compensation systems, in asset-backed security design, and are being considered for use in setting regulatory capital requirements for banks. This paper empirically examines properties of the major methods currently used to estimate average default probabilities by grade. Evidence of potential problems of bias, instability, and gaming is presented. With care, and perhaps judicious application of multiple methods, satisfactory estimates may be possible. In passing, evidence is presented about other properties of internal and rating-agency ratings.     

Forward–futures price differences in the UK commercial property market: Arbitrage and marking-to-model explanations

In this paper the differences between forward and futures prices for the UK commercial property market are analyzed, using both time series and panel data. A first battery of tests establishes that the observed differences are statistically significant over the study period. Further analysis considers the modeling of this difference using mean-reverting models. The proposed models are then estimated with a number of alternative estimation methods and second stage statistical tests are implemented in order to decide which model and estimation method best represent the data.     

Valuation of American options on foreign currency

Pricing models for American call and put options on foreign currency are derived herein. These models are used to investigate the efficiency of the market for foreign currency options. The evidence presented here indicates that market prices for these options deviate substantially from their corresponding model prices. In addition, it is shown that a hedging strategy executed at transaction prices can be used to translate an observed deviation of market from model prices into positive excess profits. However, these profits are eliminated if the strategy is executed at bid and offer prices.     

Dynamics of credit spread moments of European corporate bond indexes

Traditional quantitative credit risk models assume that changes in credit spreads are normally distributed but empirical evidence shows that they are likely to be skewed, fat-tailed, and change behaviour over time. Not taking into account such characteristics can compromise calculation of loss probabilities, pricing of credit derivatives, and profitability of trading strategies. Therefore, the aim of this study is to investigate the dynamics of higher moments of changes in credit spreads of European corporate bond indexes using extensions of GARCH type models that allow for time-varying volatility, skewness and kurtosis of changes in credit spreads as well as a regime-switching GARCH model which allows for regime shifts in the volatility of changes in credit spreads. Performance evaluation methods are used to assess which model captures the dynamics of observed distribution of the changes in credit spreads, produces superior volatility forecasts and Value-at-Risk estimates, and yields profitable trading strategies. The results presented can have significant implications for risk management, trading activities, and pricing of credit derivatives.     

The Impact of the Definition of Inflation on the Effectiveness of Inflation Accounting Adjustments

In tests of inflation accounting methods, inflation is generally seen as a simple phenomenon: the prices of all elements change at the same rate. The example presented here deals with a different case: inflation is characterized by changes in the structure of prices. In particular, prices of articles bought and articles sold do not vary at the same rates.
In this context, it is observed that three types of adjustments are not effective, i.e. they do not have the potential to report real or nominal rates of return. This result should be considered as a criticism of the coherence of inflation accounting methods.     

Nonlinear dynamical structural equation models

Structural equation models (SEMs) have been widely used in behavioural, educational, medical and socio-psychological research for exploring and confirming relations among observed and latent variables. In the existing SEMs, the unknown coefficients in the measurement and structural equations are assumed to be constant with respect to time. This assumption does not always hold, as the relation among the observed and latent variables varies with time for some situations. In this paper, we propose nonlinear dynamical structural equation models to cope with these situations, and explore the nonlinear dynamic of the relation between the variables involved. A local maximum likelihood-based estimation procedure is proposed. We investigate a bootstrap resampling-based test for the hypothesis that the coefficient is constant with respect to time, as well as confidence bands for the unknown coefficients. Intensive simulation studies are conducted to show the empirical performance of the proposed estimation procedure, hypothesis test statistic and confidence band. Finally, a real example in relation to the stock market of Hong Kong is presented to demonstrate the proposed methodologies.     

Identification-robust analysis of DSGE and structural macroeconomic models

Full- and limited-information identification-robust methods are proposed for structural systems, notably DSGE models, which are valid whether identification is weak or strong, theory-intrinsic or data-specific. The proposed methods are applied to a standard New Keynesian system for the U.S. Single- and multi-equation estimation and fit are also compared. When a unique rational-expectation stable equilibrium is imposed, the model is rejected. In contrast, limited-information inference produces informative results regarding forward-looking behavior in the NKPC and precise conclusions on feedback coefficients in the reaction function, which cannot be reached via single-equation methods.     

Numerical computation of Theta in a jump-diffusion model by integration by parts

Using the Malliavin calculus in time inhomogeneous jump-diffusion models, we obtain an expression for the sensitivity Theta of an option price (with respect to maturity) as the expectation of the option payoff multiplied by a stochastic weight. This expression is used to design efficient numerical algorithms that are compared with traditional finite-difference methods for the computation of Theta. Our proof can be viewed as a generalization of Dupire's integration by parts to arbitrary and possibly non-smooth payoff functions. In the time homogeneous case, Theta admits an expression from the Black–Scholes PDE in terms of Delta and Gamma but the representation formula obtained in this way is different from ours. Numerical simulations are presented in order to compare the efficiency of the finite-difference and Malliavin methods.     

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.     

Pricing options on scenario trees

We examine valuation procedures that can be applied to incorporate options in scenario-based portfolio optimization models. Stochastic programming models use discrete scenarios to represent the stochastic evolution of asset prices. At issue is the adoption of suitable procedures to price options on the basis of the postulated discrete distributions of asset prices so as to ensure internally consistent portfolio optimization models. We adapt and implement two methods to price European options in accordance with discrete distributions represented by scenario trees and assess their performance with numerical tests. We consider features of option prices that are observed in practice. We find that asymmetries and/or leptokurtic features in the distribution of the underlying materially affect option prices; we quantify the impact of higher moments (skewness and excess kurtosis) on option prices. We demonstrate through empirical tests using market prices of the S&P500 stock index and options on the index that the proposed procedures consistently approximate the observed prices of options under different market regimes, especially for deep out-of-the-money options.     

Modeling time series information into option prices: An empirical evaluation of statistical projection and GARCH option pricing model

This paper compares the empirical performances of statistical projection models with those of the Black–Scholes (adapted to account for skew) and the GARCH option pricing models. Empirical analysis on S&P500 index options shows that the out-of-sample pricing and projected trading performances of the semi-parametric and nonparametric projection models are substantially better than more traditional models. Results further indicate that econometric models based on nonlinear projections of observable inputs perform better than models based on OLS projections, consistent with the notion that the true unobservable option pricing model is inherently a nonlinear function of its inputs. The econometric option models presented in this paper should prove useful and complement mainstream mathematical modeling methods in both research and practice.     

Univariate detrending methods with stochastic trends

This paper discusses detrending economic time series, when the trend is modelled as a stochastic process. It considers unobserved components models in which the observed series is decomposed into a trend (a random walk with drift) and a residual stationary component. Optimal detrending methods are discussed, as well as problems associated with using these detrended data in regression models. The methods are applied to three time series: GNP, disposable income, and consumption expenditures. The detrended data are used to test a version of the Life Cycle consumption model.     

Earnings management surrounding CEO changes

This paper investigates the extent of earnings management in the periods surrounding CEO changes by Australian firms. Evidence is presented of incoming CEOs undertaking earnings management to reduce income in the year of CEO change, with abnormal and extraordinary items being the primary vehicle through which this is achieved. This result is consistent with the notion of new CEOs engaging in an 'earnings bath', and is strongest for non–routine CEO changes, where the opportunities to manage earnings are greatest. Extending prior work, classification of CEO changes as routine or non–routine is based on an expanded information search, and this provides insights into the CEO change process and identifies problems with simpler mechanistic classification methods. Additionally, detailed information of the operation of the modified Jones model for estimating expected accruals is presented, and this is consistent with such models having low explanatory power in identifying abnormal accruals.     

Information criteria for GARCH model selection

In this paper, a set of appropriately modified information criteria for selection of models from the AR-GARCH class is derived. It is argued that unmodified or naively modified traditional information criteria cannot be used for order determination in the context of conditionally heteroscedastic models. The models selected using the modified criteria are then used to forecast both the conditional mean and the conditional variance of two high frequency exchange rate series. The analysis indicates that although the use of such model selection methods does lead to significantly improved forecasting accuracies for the conditional variance in some instances, these improvements are by no means universal. The use of these criteria to jointly select conditional mean and conditional variance model orders leads to performance degradation for the conditional mean forecasts compared to models which do not allow for the heteroscedasticity.     

A survey of models for determining optimal audit strategies

The problem studied in this survey is how to optimize the allocation of audit resources over an auditee population with respect to available population statistics. The auditees are assumed to optimize their expected utility based on information about the audit strategy. This survey is limited to models where the auditee can vary the fraud amount along a continuous scale.If the auditor is not able or willing to announce the audit strategy, a Nash equilibrium can be derived in which the auditor and auditee correctly anticipate each other's strategies. If the auditor announces the audit strategy in advance, the problem is formulated as a sequential game with perfect information which is solved as an optimization problem.Early models in the literature resulted in unrealistically high degrees of fraud. Later models have incorporated a split into one group of inherently honest auditees and another group of potentially dishonest auditees. The fraction of inherently honest auditees is exogenous.In this paper, the four combinations of non-announcing/pre-announcing the strategy and all potentially dishonest/some inherently honest auditees are studied. For the case of pre-announcing the strategy with some inherently honest auditees, two new solution methods are presented.Two main conclusions are as follows. First, models with some inherently honest auditees have greater external validity. Second, when a pre-announced strategy is feasible, as it often is with tax and benefit audits, the pre-announced strategy is preferred by the auditor over the non-announced strategy.     

Dynamic stochastic general equilibrium (DSGE) modelling in practice: identification,estimation and evaluation

In recent years, dynamic stochastic general equilibrium (DSGE) models have come to play an increasing role in central banks, as an aid in the formulation of monetary policy (and increasingly after the global crisis, for maintaining financial stability). DSGE models, compared to other widely prevalent econometric models (such as vector autoregressive or large-scale econometric models), are less a-theoretic and with secure micro-foundations based on the optimizing behaviour of rational economic agents. Additionally, the models in spite of being strongly tied to theory, can be ‘taken to the data’ in a meaningful way. A major feature of these models is that their theoretical underpinnings lie in what has now come to be called as the New Consensus Macroeconomics (NCM). This paper concentrates on the econometric structure underpinning such models. Identification, estimation and evaluation issues are discussed at length with a special emphasis on the role of Bayesian maximum likelihood methods.     

A variance reduction technique based on integral representations

Abstract

Standard Monte Carlo methods can often be significantly improved with the addition of appropriate variance reduction techniques. In this paper a new and powerful variance reduction technique is presented. The method is based directly on the Itô calculus and is used to find unbiased variance-reduced estimators for the expectation of functionals of Itô diffusion processes. The approach considered has wide applicability: for instance, it can be used as a means of approximating solutions of parabolic partial differential equations or applied to valuation problems that arise in mathematical finance. We illustrate how the method can be applied by considering the pricing of European-style derivative securities for a class of stochastic volatility models, including the Heston model.     

The use of credit scoring in the mortgage industry

In times of increased focus on risk management, acquiring or growing comparatively low risk mortgage portfolios has become an attractive value proposition. Banks that pursue an aggressive growth strategy in this sector, do, however, require risk control mechanisms that enable them to make a clear judgment on how great a growth appetite they can afford to have in order to still grow profitably. Moreover, under Basel II, the proper quantification of mortgage portfolio risk tends to help the release of own capital, because the mortgage portfolio is one of those portfolios where the relative benefits of internal ratings-based approaches compared with the standardised approach are greatest. Credit scoring models in general, and credit scorecards in particular, are suitable methods for quantifying the risk of an individual mortgage applicant or mortgage customer. In addition to score card development, this paper reviews alternative scoring model types that could be used for mortgage scoring. It presents reasons why it is beneficial to build such models in-house, before focusing on the steps necessary for building a mortgage scorecard. Finally, it discusses the important topics of creating segments, deploying models and eventually monitoring models.     

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.