NCER Working Paper Series

2013

• #99
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  JEL-Codes:

  C22; G11; G17

  Keywords:

  Volatility, multivariate GARCH, portfolio allocation

  On the Benefits of Equicorrelation for Portfolio Allocation

  Adam Clements, Ayesha Scott and Annastiina Silvennoinen

  The importance of modelling correlation has long been recognised in the field of portfolio management with large dimensional multivariate problems are increasingly becoming the focus of research. This paper provides a straightforward and commonsense approach toward investigating a number of models used to generate forecasts of the correlation matrix for large dimensional problems. We find evidence in favour of assuming equicorrelation across various portfolio sizes, particularly during times of crisis. During periods of market calm however, the suitability of the constant conditional correlation model cannot be discounted especially for large portfolios. A portfolio allocation problem is used to compare forecasting methods. The global minimum variance portfolio and Model Confidence Set are used to compare methods, whilst portfolio weight stability and relative economic value are also considered.

• #98
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  JEL-Codes:

  C22

  Keywords:

  Credit risk, Merton model, Stochastic volatility, Particle Filtter; Default probability, CDS

  Structural Credit Risk Model with Stochastic Volatility: A Particle-filter Approach

  Di Bu and Yin Liao

  This paper extends Merton's structural credit risk model to account for the fact that the firm's asset volatility follows a stochastic process. With the presence of stochastic volatility, the transformed-data maximum likelihood estimation (MLE) method of Duan (1994, 2000) can no longer be applied to estimate the model. We devise a particle filtering algorithm to solve this problem. This algorithm is based on the general non-linear and non-Gaussian filtering with sequential parameter learning, and a simulation study is conducted to ascertain its finite sample performance. Meanwhile, we implement this model on the real data of companies in Dow Jones industrial average and find that incorporating stochastic volatility into the structural model can largely improve the model performance.

• #97
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  JEL-Codes:

  C32; C36; C51

  Keywords:

  Mixed models, transitory shocks, mixed shocks, long-run restrictions, sign restrictions, instrumental variables

  Econometric Issues when Modelling with a Mixture of I(1) and I(0) Variables

  Lance A Fisher, Syeon-seung Huh and Adrian Pagan

  This paper considers structural models when both I(1) and I(0) variables are present. It is necessary to extend the traditional classification of shocks as permanent and transitory, and we do this by introducing a mixed shock. The extra shocks coming from introducing I(0) variables into a system are then classified as either mixed or transitory. Conditions are derived upon the nature of the SVAR in the event that these extra shocks are transitory. We then analyse what happens when there are mixed shocks, finding that it changes a number of ideas that have become established from the cointegration literature. The ideas are illustrated using a well-known SVAR where there are mixed shocks. This SVAR is re-formulated so that the extra shocks coming from the introduction of I(0) variables do not affect relative prices in the long-run and it is found that this has major implications for whether there is a price puzzle. It is also shown how to handle long-run parametric restrictions when some shocks are identified using sign restrictions.

• #96
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  Keywords:

  pattern recognition, pattern matching, pattern formation

  Patterns and Their Uses

  Adrian Pagan

  Three major themes have emerged in the literature on patterns. These involve pattern recognition, pattern matching (do a set of observations match a particular pattern?) and pattern formation ( how does a pattern emerge?). The talk takes up each of these themes, presenting some economic examples of where a pattern has been of interest, how it has been measured (section 2), some issues in checking whether a given pattern holds (section 3), what theories might account for a particular pattern (section 4), and the predictability of patterns ( section5). Most attention is paid to judging macroeconomic models based on their ability to generate macroeconomic and financial patterns, and some simple tests are suggested to do this. Because sentiment and the origins of patterns are so inextricably linked in macroeconomics and .finance we will spend some time looking at the literature which deals with the interaction of series representing sentiment with those representing macroeconomic and financial outcomes.

• #94
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  Keywords:

  Phillips Curve, structural change

  Issues in Estimating New Keynesian Phillips Curves in the Presence of Unknown Structural Change

  Mariano Kulish and Adrian Pagan

  Many papers which have estimated models with forward looking expectations have reported that the magnitude of the coefficients of the expectations term is very large when compared with the effects coming from past dynamics. This has sometimes been regarded as implausible and led to the feeling that the expectations coefficient is biased upwards. A relatively general argument that has been advanced is that the bias could be due to structural changes in the means of the variables entering the structural equation. An alternative explanation is that the bias comes from weak instruments. In this paper we investigate the issue of upward bias in the estimated coefficients of the expectations variable based on a model where we can see what causes the breaks and how to control for them. We conclude that weak instruments are the most likely cause of any bias and note that structural change can affect the quality of instruments. We also look at some empirical work in Castle et al. (2011) on the NK Phillips curve in the Euro Area and U.S, assessing whether the smaller coefficient on expectations that Castle et al. (2011) highlight is due to structural change. Our conclusion is that it is not. Instead it comes from their addition of variables to the NKPC. After allowing for the fact that there are weak instruments in the estimated re-specified model it would seem that the forward coefficient estimate is actually quite high rather than low.

• #93
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  JEL-Codes:

  C22; G00

  Keywords:

  Realized volatility, diffusion, jumps, point process, Hawkes process, forecasting

  Modeling and forecasting realized volatility: getting the most out of the jump component

  Adam E Clements and Yin Liao

  Modeling and forecasting realized volatility is of paramount importance. Recent econometric developments allow total volatility to be decomposed into its' constituent continuous and jump components. While previous studies have examined the role of both components in forecasting, little analysis has been undertaken into how best to harness the jump component. This paper considers how to get the most out of the jump component for the purposes of forecasting total volatility. In combination with the magnitude of past jumps, the intensity of jump occurrence is examined. Estimated jump intensity from a point process model is used within a forecasting regression framework. Even in the presence of the diffusive part of total volatility, and past jump size, intensity is found to significantly improve forecast accuracy. The improvement is particularly apparent on the days when jumps occur or when markets are turbulent. Overall, the best way to harness the jump component for volatility forecasting is to make use of both the magnitude and probability of jump occurrences.

• #92
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  JEL-Codes:

  L83;D63;C63

  Keywords:

  Competitive balance, Idealized standard deviation, Ratio of standard, deviations, Season length, Sports economics, Simulation

  Competitive Balance Measures in Sports Leagues: The Effects of Variation in Season Length

  P Dorian Owen and Nicholas King

  Appropriate measurement of competitive balance is a cornerstone of the economic analysis of professional sports leagues. We examine the distributional properties of the ratio of standard deviations (RSD) of points percentages, the most widely used measure of competitive balance in the sports economics literature, in comparison with other standard-deviation-based measures. Simulation methods are used to evaluate the effects of changes in season length on the distributions of competitive balance measures for different distributions of the strengths of teams in a league. The popular RSD measure performs as expected only in cases of perfect balance; if there is imbalance in team strengths, its distribution is very sensitive to changes in season length. This has important implications for comparisons of competitive balance for different sports leagues with different numbers of teams and/or games played.

• #91
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  JEL-Codes:

  C22;G00

  Keywords:

  Realized volatility, correlation, jumps, co-jumps, point process

  The dynamics of co-jumps, volatility and correlation

  Adam Clements and Yin Liao

  Understanding the dynamics of volatility and correlation is a crucially important issue. The literature has developed rapidly in recent years with more sophisticated estimates of volatility, and its associated jump and diffusion components. Previous work has found that jumps at an index level are not related to future volatility. Here we examine the links between co-jumps within a group of large stocks, the volatility of, and correlation between their returns. It is found that the occurrence of common, or co-jumps between the stocks are unrelated to the level of volatility or correlation. On the other hand, both volatility and correlation are lower subsequent to a co-jump. This indicates that co-jumps are a transient event but in contrast to earlier research have a greater impact that jumps at an index level.

• #90
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  JEL-Codes:

  Fourier transform, Fourier series, characteristic function, option price

  On the Efficacy of Fourier Series Approximations for Pricing European and Digital Options

  A S Hurn, Kenenth A Lindsay and Andrew McClelland

  This paper investigates several competing procedures for computing the price of European and digital options in which the underlying model has a characteristic function that is known in at least semi-closed form. The algorithms for pricing the options investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. The performance of the algorithms is assessed in simulation experiments which price options in a Black-Scholes world where an analytical solution is available and for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the half-range cosine series and the full-range Fourier series. There are however two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together, these two conclusions make a strong case for the merit of pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series.

• #89
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  JEL-Codes:

  C33; E31; R19

  Keywords:

  Relative price convergence; Structural break; Panel unit root test; Half-life; Time

  City Relative Price Dynamics in Australia: Are Structural Breaks Important?

  Hiranya K Nath and Jayanta Sarkar

  This paper examines the dynamic behaviour of relative prices across seven Australian cities by applying panel unit root test procedures with structural breaks to quarterly CPI data for 1972Q1-2011Q4. We find overwhelming evidence of convergence in city relative prices. Three common structural breaks are endogenously determined at 1985, 1995, and 2007. Further, correcting for two potential biases, namely Nickell bias and time aggregation bias, we obtain half-life estimates of 2.3-3.8 quarters that are much shorter than those reported by previous research. Thus, we conclude that both structural breaks and bias corrections are important to obtain shorter half-life estimates.