Testing threshold functions using implied minterm structure

A geometrical structure called the implied minterm structure (IMS) has been developed from the properties of minterms of a threshold function. The IMS is useful for the manual testing of linear separability of switching functions of up to six variables. This testing is done just by inspection of the plot of the function on the IMS.

Genomic inflation factors under polygenic inheritance

Population structure, including population stratification and cryptic relatedness, can cause spurious associations in genome-wide association studies (GWAS). Usually, the scaled median or mean test statistic for association calculated from multiple single-nucleotide-polymorphisms across the genome is used to assess such effects, and 'genomic control' can be applied subsequently to adjust test statistics at individual loci by a genomic inflation factor. Published GWAS have clearly shown that there are many loci underlying genetic variation for a wide range of complex diseases and traits, implying that a substantial proportion of the genome should show inflation of the test statistic. Here, we show by theory, simulation and analysis of data that in the absence of population structure and other technical artefacts, but in the presence of polygenic inheritance, substantial genomic inflation is expected. Its magnitude depends on sample size, heritability, linkage disequilibrium structure and the number of causal variants. Our predictions are consistent with empirical observations on height in independent samples of ~4000 and ~133,000 individuals.

Dynamics of inflation expectations in the euro area

The present study examines empirically the inflation dynamics of the euro area. The focus of the analysis is on the role of expectations in the inflation process. In six articles we relax rationality assumption and proxy expectations directly using OECD forecasts or Consensus Economics survey data. In the first four articles we estimate alternative Phillips curve specifications and find evidence that inflation cannot instantaneously adjust to changes in expectations. A possible departure of expectations from rationality seems not to be powerful enough to totally explain the persistence of euro area inflation in the New Keynesian framework. When expectations are measured directly, the purely forward-looking New Keynesian Phillips curve is outperformed by the hybrid Phillips curve with an additional lagged inflation term and the New Classical Phillips curve with a lagged expectations term. The results suggest that the euro area inflation process has become more forward-looking in the recent years of low and stable inflation. Moreover, in low inflation countries, the inflation dynamics have been more forward-looking already since the late 1970s. We find evidence of substantial heterogeneity of inflation dynamics across the euro area countries. Real time data analysis suggests that in the euro area real time information matters most in the expectations term in the Phillips curve and that the balance of expectations formation is more forward- than backward-looking. Vector autoregressive (VAR) models of actual inflation, inflation expectations and the output gap are estimated in the last two articles.The VAR analysis indicates that inflation expectations, which are relatively persistent, have a significant effect on output. However,expectations seem to react to changes in both output and actual inflation, especially in the medium term. Overall, this study suggests that expectations play a central role in inflation dynamics, which should be taken into account in conducting monetary policy.

Non-Gaussian Cosmological Perturbations from Hybrid Inflation and Preheating

This thesis consists of four research papers and an introduction providing some background. The structure in the universe is generally considered to originate from quantum fluctuations in the very early universe. The standard lore of cosmology states that the primordial perturbations are almost scale-invariant, adiabatic, and Gaussian. A snapshot of the structure from the time when the universe became transparent can be seen in the cosmic microwave background (CMB). For a long time mainly the power spectrum of the CMB temperature fluctuations has been used to obtain observational constraints, especially on deviations from scale-invariance and pure adiabacity. Non-Gaussian perturbations provide a novel and very promising way to test theoretical predictions. They probe beyond the power spectrum, or two point correlator, since non-Gaussianity involves higher order statistics. The thesis concentrates on the non-Gaussian perturbations arising in several situations involving two scalar fields, namely, hybrid inflation and various forms of preheating. First we go through some basic concepts -- such as the cosmological inflation, reheating and preheating, and the role of scalar fields during inflation -- which are necessary for the understanding of the research papers. We also review the standard linear cosmological perturbation theory. The second order perturbation theory formalism for two scalar fields is developed. We explain what is meant by non-Gaussian perturbations, and discuss some difficulties in parametrisation and observation. In particular, we concentrate on the nonlinearity parameter. The prospects of observing non-Gaussianity are briefly discussed. We apply the formalism and calculate the evolution of the second order curvature perturbation during hybrid inflation. We estimate the amount of non-Gaussianity in the model and find that there is a possibility for an observational effect. The non-Gaussianity arising in preheating is also studied. We find that the level produced by the simplest model of instant preheating is insignificant, whereas standard preheating with parametric resonance as well as tachyonic preheating are prone to easily saturate and even exceed the observational limits. We also mention other approaches to the study of primordial non-Gaussianities, which differ from the perturbation theory method chosen in the thesis work.

A Cointegration Approach to Topics in Empirical Macroeconomics (summary section only)

Mikael Juselius’ doctoral dissertation covers a range of significant issues in modern macroeconomics by empirically testing a number of important theoretical hypotheses. The first essay presents indirect evidence within the framework of the cointegrated VAR model on the elasticity of substitution between capital and labor by using Finnish manufacturing data. Instead of estimating the elasticity of substitution by using the first order conditions, he develops a new approach that utilizes a CES production function in a model with a 3-stage decision process: investment in the long run, wage bargaining in the medium run and price and employment decisions in the short run. He estimates the elasticity of substitution to be below one. The second essay tests the restrictions implied by the core equations of the New Keynesian Model (NKM) in a vector autoregressive model (VAR) by using both Euro area and U.S. data. Both the new Keynesian Phillips curve and the aggregate demand curve are estimated and tested. The restrictions implied by the core equations of the NKM are rejected on both U.S. and Euro area data. These results are important for further research. The third essay is methodologically similar to essay 2, but it concentrates on Finnish macro data by adopting a theoretical framework of an open economy. Juselius’ results suggests that the open economy NKM framework is too stylized to provide an adequate explanation for Finnish inflation. The final essay provides a macroeconometric model of Finnish inflation and associated explanatory variables and it estimates the relative importance of different inflation theories. His main finding is that Finnish inflation is primarily determined by excess demand in the product market and by changes in the long-term interest rate. This study is part of the research agenda carried out by the Research Unit of Economic Structure and Growth (RUESG). The aim of RUESG it to conduct theoretical and empirical research with respect to important issues in industrial economics, real option theory, game theory, organization theory, theory of financial systems as well as to study problems in labor markets, macroeconomics, natural resources, taxation and time series econometrics. RUESG was established at the beginning of 1995 and is one of the National Centers of Excellence in research selected by the Academy of Finland. It is financed jointly by the Academy of Finland, the University of Helsinki, the Yrjö Jahnsson Foundation, Bank of Finland and the Nokia Group. This support is gratefully acknowledged.

Modeling and Forecasting Implied Volatility: Implications for Trading, Pricing, and Risk Management

Modeling and forecasting of implied volatility (IV) is important to both practitioners and academics, especially in trading, pricing, hedging, and risk management activities, all of which require an accurate volatility. However, it has become challenging since the 1987 stock market crash, as implied volatilities (IVs) recovered from stock index options present two patterns: volatility smirk(skew) and volatility term-structure, if the two are examined at the same time, presents a rich implied volatility surface (IVS). This implies that the assumptions behind the Black-Scholes (1973) model do not hold empirically, as asset prices are mostly influenced by many underlying risk factors. This thesis, consists of four essays, is modeling and forecasting implied volatility in the presence of options markets’ empirical regularities. The first essay is modeling the dynamics IVS, it extends the Dumas, Fleming and Whaley (DFW) (1998) framework; for instance, using moneyness in the implied forward price and OTM put-call options on the FTSE100 index, a nonlinear optimization is used to estimate different models and thereby produce rich, smooth IVSs. Here, the constant-volatility model fails to explain the variations in the rich IVS. Next, it is found that three factors can explain about 69-88% of the variance in the IVS. Of this, on average, 56% is explained by the level factor, 15% by the term-structure factor, and the additional 7% by the jump-fear factor. The second essay proposes a quantile regression model for modeling contemporaneous asymmetric return-volatility relationship, which is the generalization of Hibbert et al. (2008) model. The results show strong negative asymmetric return-volatility relationship at various quantiles of IV distributions, it is monotonically increasing when moving from the median quantile to the uppermost quantile (i.e., 95%); therefore, OLS underestimates this relationship at upper quantiles. Additionally, the asymmetric relationship is more pronounced with the smirk (skew) adjusted volatility index measure in comparison to the old volatility index measure. Nonetheless, the volatility indices are ranked in terms of asymmetric volatility as follows: VIX, VSTOXX, VDAX, and VXN. The third essay examines the information content of the new-VDAX volatility index to forecast daily Value-at-Risk (VaR) estimates and compares its VaR forecasts with the forecasts of the Filtered Historical Simulation and RiskMetrics. All daily VaR models are then backtested from 1992-2009 using unconditional, independence, conditional coverage, and quadratic-score tests. It is found that the VDAX subsumes almost all information required for the volatility of daily VaR forecasts for a portfolio of the DAX30 index; implied-VaR models outperform all other VaR models. The fourth essay models the risk factors driving the swaption IVs. It is found that three factors can explain 94-97% of the variation in each of the EUR, USD, and GBP swaption IVs. There are significant linkages across factors, and bi-directional causality is at work between the factors implied by EUR and USD swaption IVs. Furthermore, the factors implied by EUR and USD IVs respond to each others’ shocks; however, surprisingly, GBP does not affect them. Second, the string market model calibration results show it can efficiently reproduce (or forecast) the volatility surface for each of the swaptions markets.

Price Inflation, Unemployment and Devaluations: The Finnish Experience of the 1990s

In this paper I provide some empirical answers to important questions such as the determinants of price inflation and the role of inflation polices. The results indicate that monetary policy is surprisingly impotent as a device for controlling inflation and there is little support that it influences the real variables. The low inflation after the Finnish devaluations in the beginning of 90s is foremost due to a previous imbalance in the labor markets and depressed aggregate demand.

Maximum Loss Calculation using Scenario Analysis, Heavy Tails and Implied Volatility Patterns

The objective of this paper is to improve option risk monitoring by examining the information content of implied volatility and by introducing the calculation of a single-sum expected risk exposure similar to the Value-at-Risk. The figure is calculated in two steps. First, there is a need to estimate the value of a portfolio of options for a number of different market scenarios, while the second step is to summarize the information content of the estimated scenarios into a single-sum risk measure. This involves the use of probability theory and return distributions, which confronts the user with the problems of non-normality in the return distribution of the underlying asset. Here the hyperbolic distribution is used to describe one alternative for dealing with heavy tails. Results indicate that the information content of implied volatility is useful when predicting future large returns in the underlying asset. Further, the hyperbolic distribution provides a good fit to historical returns enabling a more accurate definition of statistical intervals and extreme events.

Unrealized expectations of jumps in volatility: An explanation to the low and time-varying predictive power of implied volatility

The low predictive power of implied volatility in forecasting the subsequently realized volatility is a well-documented empirical puzzle. As suggested by e.g. Feinstein (1989), Jackwerth and Rubinstein (1996), and Bates (1997), we test whether unrealized expectations of jumps in volatility could explain this phenomenon. Our findings show that expectations of infrequently occurring jumps in volatility are indeed priced in implied volatility. This has two important consequences. First, implied volatility is actually expected to exceed realized volatility over long periods of time only to be greatly less than realized volatility during infrequently occurring periods of very high volatility. Second, the slope coefficient in the classic forecasting regression of realized volatility on implied volatility is very sensitive to the discrepancy between ex ante expected and ex post realized jump frequencies. If the in-sample frequency of positive volatility jumps is lower than ex ante assessed by the market, the classic regression test tends to reject the hypothesis of informational efficiency even if markets are informationally effective.

Fiscal imbalances, inflation and sovereign default dynamics

Resumen: La cuestión central que este artículo busca responder es como la política monetaria puede afectar el comportamiento de equilibrio de primas por riesgo soberano y cesación de pagos. El artículo se basa en el modelo de “una-tasa-interés”. La deuda pública se hace riesgosa a causa de una política fiscal activa, como en Uribe (2006), reflejando la habilidad limitada de la autoridad fiscal para controlar el superávit primario. El problema de insolvencia es debido a una oleada de mala suerte (shocks negativos que afectan el superávit primario). Pero en contraste a los resultados de Uribe, a medida que aumenta el costo de la deuda soberana (que resulta de un excedente primario débil), la cesación de pagos se anticipa y es reflejada por una creciente prima de riesgo en el país y una probabilidad de cesación de pagos. La cesación de pagos se define como un incumplimiento de un acuerdo contractual y por ende la decisión es tomada por la autoridad fiscal. Mientras tanto, objetivos conflictivos entre la autoridad monetaria y fiscal juegan un rol importante en llevar a la autoridad fiscal a la cesación de pagos sobre sus pasivos. La característica de la política del gobierno necesaria para restaurar el equilibrio después de la cesación de pagos también es analizada.

The New Keynesian Monetary Model: Does it Show the Comovement Between Output and Inflation in the U.S.?

Published as article in: Journal of Economic Dynamics and Control (2008), 32(May), pp. 1466-1488.

Testing the Forecasting Performance of Ibex 35 Option-implied Risk-neutral Densities

Published also as: Documento de Trabajo Banco de España 0504/2005.

Option-Implied Preferences Adjustments and Risk-Neutral Density Forecasts

The main objective of this paper is to analyse the value of information contained in prices of options on the IBEX 35 index at the Spanish Stock Exchange Market. The forward looking information is extracted using implied risk-neutral density functions estimated by a mixture of two-lognormals and three alternative risk-adjustments: the classic power and exponential utility functions and a habit-based specification that allows for a counter-cyclical variation of risk aversion. Our results show that at four-week horizon we can reject the hypothesis that between October 1996 and March 2000 the risk-neutral densities provide accurate predictions of the distributions of future realisations of the IBEX 35 index at a four-week horizon. When forecasting through risk-adjusted densities the performance of this period is statistically improved and we no longer reject that hypothesis. All risk-adjusted densities generate similar forecasting statistics. Then, at least for a horizon of four-weeks, the actual risk adjustment does not seem to be the issue. By contrast, at the one-week horizon risk-adjusted densities do not improve the forecasting ability of the risk-neutral counterparts.

Explosive Hyperinflation, Inflation Tax Laffer Curve and Modelling the use of Money

This paper analyzes the existence of an inflation tax Laffer curve (ITLC) in the context of two standard optimizing monetary models: a cash-in-advance model and a money in the utility function model. Agents’ preferences are characterized in the two models by a constant relative risk aversion utility function. Explosive hyperinflation rules out the presence of an ITLC. In the context of a cash-in-advance economy, this paper shows that explosive hyperinflation is feasible and thus an ITLC is ruled out whenever the relative risk aversion parameter is greater than one. In the context of an optimizing model with money in the utility function, this paper firstly shows that an ITLC is ruled out. Moreover, it is shown that explosive hyperinflations are more likely when the transactions role of money is more important. However, hyperinflationary paths are not feasible in this context unless certain restrictions are imposed.