A Comparison of Univariate Stochastic Volatility Models for U.S. Short Rates Using EMM Estimation

In this paper, the efficient method of moments (EMM) estimation using a seminonparametric (SNP) auxiliary model is employed to determine the best fitting model for the volatility dynamics of the U.S. weekly three-month interest rate. A variety of volatility models are considered, including one-factor diffusion models, two-factor and three-factor stochastic volatility (SV) models, non-Gaussian diffusion models with Stable distributed errors, and a variety of Markov regime switching (RS) models. The advantage of using EMM estimation is that all of the proposed structural models can be evaluated with respect to a common auxiliary model. We find that a continuous-time twofactor SV model, a continuous-time three-factor SV model, and a discrete-time RS-involatility model with level effect can well explain the salient features of the short rate as summarized by the auxiliary model. We also show that either an SV model with a level effect or a RS model with a level effect, but not both, is needed for explaining the data. Our EMM estimates of the level effect are much lower than unity, but around 1/2 after incorporating the SV effect or the RS effect.

Mineral Asset Valuation Under Economic Uncertainty: A Complex System for Operational Flexibility

The global mineral industry faces constant challenges that are incited and intensified by market uncertainty. Demand constrictions, resource scarcity, and market volatility all generate market risk that is compounded by the high capital and long payback periods inherent to mining projects. Quantitative risk assessments provide a methodology to leverage uncertain economic scenarios and accurately assess profitability; however, current mine valuation techniques and engineering economic approaches tend to scrutinize the uncertainty of technical factors, such as ore grade and metallurgical recovery, to a much greater degree than market factors, like price-demand restrictions. Nevertheless, the optimal operating conditions for mining, mineral processing and refining must reflect the true dynamics of uncertain commodity prices, and typical operational responses, such as modifications to mine production and material stockpiling.;This thesis presents a new mineral asset valuation methodology based on economic uncertainty in the commodity market and operational flexibility for mining operations. This novel valuation approach resulted in the generation of a complex system that consists of three primary components. First, a price forecasting component was used to generate future commodity price scenarios with two different stochastic differential equation models (Geometric Brownian Motion and Mean-Reverting-drift). Second, a dynamic methodology of discounted cash flow (DCF) was developed, allowing operational flexibility for mining, processing, stockpiling, and selling material. Third, two distinct optimization techniques (Interior-point method and genetic algorithms) were applied for identification of optimal operating parameters in a mining operation, with a particular focus on using buffer stockpiles to ameliorate the impacts of volatile price fluctuations. The dynamic model was applied in a case study assessing the valuation of a greenfield Ni-Co-Sc mine project. The hypothetical deposit was subjected to different levels of commodity price trends, price volatility, discount rates and maximum stockpiling capacity. Overall, the dynamic valuation model obtained NPV results ranging from 2% to 11% higher than standard static DCF techniques. Operational flexibility and ore inventory management proved to be crucial for profit increase on the project

The Probability Density Function of Interest Rates Implied in the Price of Options

The paper contributes to the stochastic volatility literature by developing simulation schemes for the conditional distributions of the price of long term bonds and their variability based on non-standard distributional assumptions and volatility concepts; it illustrates the potential value of the information contained in the prices of options on long and short term lira interest rate futures for the conduct of monetary policy in Italy, at times when significant regime shifts have occured.stochastic models, statistical analysis, interest rates, financial market

Improving market-based forecasts of short-term interest rates: time-varying stationarity and the predictive content of switching regime-expectations

Modeling short-term interest rates as following regime-switching processes has become increasingly popular. Theoretically, regime-switching models are able to capture rational expectations of infrequently occurring discrete events. Technically, they allow for potential time-varying stationarity. After discussing both aspects with reference to the recent literature, this paper provides estimations of various univariate regime-switching specifications for the German three-month money market rate and bivariate specifications additionally including the term spread. However, the main contribution is a multi-step out-of-sample forecasting competition. It turns out that forecasts are improved substantially when allowing for state-dependence. Particularly, the informational content of the term spread for future short rate changes can be exploited optimally within a multivariate regime-switching framework

Optimal funding and investment strategies in defined contribution pension plans under Epstein-Zin utility

A defined contribution pension plan allows consumption to be redistributed from the plan member’s working life to retirement in a manner that is consistent with the member’s personal preferences. The plan’s optimal funding and investment strategies therefore depend on the desired pattern of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member has an Epstein-Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution, and we also take into account the member’s human capital. We show that a stochastic lifestyling approach, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches is an optimal investment strategy. In addition, the optimal contribution rate each year is not constant over the life of the plan but reflects trade-offs between the desire for current consumption, bequest and retirement savings motives at different stages in the life cycle, changes in human capital over the life cycle, and attitude to risk

Portfolio Choice with Stochastic Investment Opportunities: a User's Guide

This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using tools from stochastic control, and how to rigorously verify their optimality by means of convex duality. Special emphasis is placed on long-horizon asymptotics, that lead to particularly tractable results.Comment: 31 pages, 4 figure

Combining long memory and level shifts in modeling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons

Combining long memory and level shifts in modeling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean- and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in high-frequency measures of volatility whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes, and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons

Temporal Issues in Market Inefficiency in asset prices with an emphasis on commodities

This summary provides an overview of the contributions made in this thesis to the literature. No references are included in the summary; these can be found in the Bibliography on page 156. This dissertation consists of 6 chapters. The first chapter acts as an introduction to the thesis and discusses the central theme of the dissertation along with providing a preview of what to expect in the following chapters. The contributions of the different chapters vary. Chapter 2 is a more introductory chapter and its contributions are perhaps less consequential than those in Chapters 3-5. Chapter 2 makes contributions to the literature on testing for explosive roots or bubbles. By modifying the Bhargava test statistic, we show in Chapter 2 that the Bhargava test can address earlier criticisms that had been cited against it; namely that it has low power when multiple bubbles are present in a particular series. Through introducing a rolling window approach, we are able to address that criticism and show that the modified Bhargava test statistic achieves better power. We compare and contrast the power of the modified test with the popular GSADF test statistic which has recently become popular in bubble testing literature. Another contribution made in this chapter is the application of these tests to a data set comprising of 25 commodities. As at the writing of the chapter this was believed to be a first attempt to perform bubble testing on a comprehensive commodity data set. Since commodities are often deemed to be targets of speculative behaviour, they are a natural universe for testing notions of market efficiency as they tend to go through different regimes through natural economic processes. Using both tests we are able to detect bubbles in similar periods with most of them being concentrated around the two oil price crises (1972-73 and 1979-80) and the financial crisis (2005-2007). Our conclusion is that the modified Bhargava statistic works better than the original statistic and can be used to complement the results of other statistics. The major contributions of Chapter 3 and 4 are the introduction of different methodologies that enable the user to assess how often asset markets are efficient. In Chapter 3 we argue that commodity prices can be estimated using switching-regression models including hidden Markov state-switching models. Instead of estimating Markov transition matrices directly from the estimation procedure, we estimate the transition matrix separately using unit root tests. By restricting the transition matrix to our estimated matrix and then estimating a Markov state-switching regression we show that we get more accurate smoothed probabilities i.e. a high probability is assigned to explosive states when the price was actually explosive and a high probability is assigned to the random walk/efficient state when the price exhibited efficient behaviour. This methodology is then extended to the three state case and it is argued that the transition matrices estimated this way will inform us of how often commodity markets are efficient. The methodology is empirically applied to non-ferrous metals with particular attention to Copper; we believe this is an additional contribution of the article. Chapter 3 also presents a partial equilibrium model which leads to an estimable reduced form expression for commodities and thereby motivates estimation by Markov switching-regressions. Three major contributions are made in Chapter 4. Firstly, we make a theoretical contribution to the literature on threshold auto-regressive models with exogenous triggers. Conditions for the existence of a mean and variance when a series follows a threshold auto-regressive (TAR) process with an exogenous trigger are derived. The second contribution is the use of TAR simulations to show that the tests which try to detect bubbles in asset prices lose a substantial amount of power when the asset price spends some time in the mean reverting state in addition to being in the explosive and random walk states. The third contribution of this article is the provision of a framework using TAR models which acts as a metric for market efficiency. By considering three states, an efficient/random walk state, a mean reverting state and an explosive state, we show that estimating asset prices as TARs with exogenous triggers can allow us to measure how often an asset market is efficient. This methodology uses a different class of models from those used in Chapter 4. The methodology is then applied to the S&P500 and FTSE100 process and it is shown that under the most general model specification, the indices primarily exhibit market efficiency. Chapter 5 looks deeper into how commodity prices are determined and thereby the main contribution is to the literature on commodity market pricing. By making three important changes to the commodity storage model of William and Wright (1991), we are able to show that our model is able to capture essential features of commodity prices that have not been captured by previous iterations. The numerical solution for the model is obtained using the Parameterized Expectations Algorithm (PEA) and simulated series based on this solution are able to reproduce some statistical features of real commodity price series including a high degree of first order auto-correlation, skewness and kurtosis. A second contribution is with regards to the application of the model; we calibrate the model to match five real commodities and show that the model’s solution is able to match real life data. The model is also able to explain why we observe spikes (bubbles) in commodity prices and cites the impact of storage as a probable contributor. Chapter 6 provides concluding remarks on the dissertation.Higher Education Commission of Pakistan, Cambridge Commonwealth Trus

Modelling electricity prices: from the state of the art to a draft of a new proposal

In the last decades a liberalization of the electric market has started; prices are now determined on the basis of contracts on regular markets and their behaviour is mainly driven by usual supply and demand forces. A large body of literature has been developed in order to analyze and forecast their evolution: it includes works with different aims and methodologies depending on the temporal horizon being studied. In this survey we depict the actual state of the art focusing only on the recent papers oriented to the determination of trends in electricity spot prices and to the forecast of these prices in the short run. Structural methods of analysis, which result appropriate for the determination of forward and future values are left behind. Studies have been divided into three broad classes: Autoregressive models, Regime switching models, Volatility models. Six fundamental points arise: the peculiarities of electricity market, the complex statistical properties of prices, the lack of economic foundations of statistical models used for price analysis, the primacy of uniequational approaches, the crucial role played by demand and supply in prices determination, the lack of clearcut evidence in favour of a specific framework of analysis. To take into account the previous stylized issues, we propose the adoption of a methodological framework not yet used to model and forecast electricity prices: a time varying parameters Dynamic Factor Model (DFM). Such an eclectic approach, introduced in the late ‘70s for macroeconomic analysis, enables the identification of the unobservable dynamics of demand and supply driving electricity prices, the coexistence of short term and long term determinants, the creation of forecasts on future trends. Moreover, we have the possibility of simulating the impact that mismatches between demand and supply have over the price variable. This way it is possible to evaluate whether congestions in the network (eventually leading black out phenomena) trigger price reactions that can be considered as warning mechanisms.