Modelling Regime‐Specific Stock Price Volatility*

Single‐state generalized autoregressive conditional heteroscedasticity (GARCH) models identify only one mechanism governing the response of volatility to market shocks, and the conditional higher moments are constant, unless modelled explicitly. So they neither capture state‐dependent behaviour of volatility nor explain why the equity index skew persists into long‐dated options. Markov switching (MS) GARCH models specify several volatility states with endogenous conditional skewness and kurtosis; of these the simplest to estimate is normal mixture (NM) GARCH, which has constant state probabilities. We introduce a state‐dependent leverage effect to NM‐GARCH and thereby explain the observed characteristics of equity index returns and implied volatility skews, without resorting to time‐varying volatility risk premia. An empirical study on European equity indices identifies two‐state asymmetric NM‐GARCH as the best fit of the 15 models considered. During stable markets volatility behaviour is broadly similar across all indices, but the crash probability and the behaviour of returns and volatility during a crash depends on the index. The volatility mean‐reversion and leverage effects during crash markets are quite different from those in the stable regime.     

Option pricing with discrete time jump processes

In this paper we propose new option pricing models based on class of models with jumps contained in the Lévy-type based models (NIG-Lévy, Schoutens, 2003, Merton-jump, Merton, 1976 and Duan based model, Duan et al., 2007). By combining these different classes of models with several volatility dynamics of the GARCH type, we aim at taking into account the dynamics of financial returns in a realistic way. The associated risk neutral dynamics of the time series models is obtained through two different specifications for the pricing kernel: we provide a characterization of the change in the probability measure using the Esscher transform and the Minimal Entropy Martingale Measure. We finally assess empirically the performance of this modelling approach, using a dataset of European options based on the S&P 500 and on the CAC 40 indices. Our results show that models involving jumps and a time varying volatility provide realistic pricing and hedging results for options with different kinds of time to maturities and moneyness. These results are supportive of the idea that a realistic time series model can provide realistic option prices making the approach developed here interesting to price options when option markets are illiquid or when such markets simply do not exist.     

Jumps in equilibrium prices and market microstructure noise

Asset prices observed in financial markets combine equilibrium prices and market microstructure noise. In this paper, we study how to tell apart large shifts in equilibrium prices from noise using high frequency data. We propose a new nonparametric test which allows us to asymptotically remove the noise from observable price data and to discover jumps in fundamental asset values. We provide its asymptotic distribution to decide when such jumps occur. In finite samples, our test offers reasonable power for distinguishing between noise and jumps. Empirical evidence indicates that it is necessary to incorporate the presence of jumps in equilibrium prices.     

A simple framework for analysing bull and bear markets

Bull and bear markets are a common way of describing cycles in equity prices. To fully describe such cycles one would need to know the data generating process (DGP) for equity prices. We begin with a definition of bull and bear markets and use an algorithm based on it to sort a given time series of equity prices into periods that can be designated as bull and bear markets. The rule to do this is then studied analytically and it is shown that bull and bear market characteristics depend upon the DGP for capital gains. By simulation methods we examine a number of DGPs that are known to fit the data quite well—random walks, GARCH models, and models with duration dependence. We find that a pure random walk provides as good an explanation of bull and bear markets as the more complex statistical models. In the final section of the paper we look at some asset pricing models that appear in the literature from the viewpoint of their success in producing bull and bear markets which resemble those in the data. Copyright © 2002 John Wiley & Sons, Ltd.     

Price Discrimination in Two‐Sided Markets

We examine the profitability and welfare implications of targeted price discrimination (PD) in two‐sided markets. First, we show that equilibrium discriminatory prices exhibit novel features relative to discriminatory prices in one‐sided models and uniform prices in two‐sided models. Second, we compare the profitability of perfect PD, relative to uniform prices in a two‐sided market. The conventional wisdom from one‐sided horizontally differentiated markets is that PD hurts the firms and benefits consumers, prisoners' dilemma. We show that PD, in a two‐sided market, may actually soften the competition. Our results suggest that the conventional advice that PD is good for competition based on one‐sided markets may not carry over to two‐sided markets.     

Spillover effects on government bond yields in euro zone. Does full financial integration exist in European government bond markets?

This paper examines the time varying nature of European government bond market integration by employing multivariate GARCH models. We state that unlike other bond markets, in euro markets the default(credit) risk factor and other macroeconomic and fiscal indicators are not able to explain the sovereign bond yields after the beginning of monetary union. This fact might be counted as a signal for perfect financial integration. However, we also find that the global shocks affect Germany and the rest of euro bond markets in various levels, creating particular discrepancies in asset prices even we take into account the market specific factors. Different level responses of each euro market to the global shocks reveal that euro bond markets are not fully integrated with each other unlike the recent literature claimed. Besides, we explore that the global factors are effective for the volatility of yield differentials among euro government bonds.     

Long‐run relations in European electricity prices

This paper analyses the interdependencies existing in wholesale electricity prices in six major European countries. The results of a robust multivariate long‐run dynamic analysis reveal the presence of four highly integrated central European markets (France, Germany, the Netherlands and Austria). The trend shared by these four electricity markets appears to be common also to gas prices, but not to oil prices. The existence of a common long‐term dynamics among electricity prices and between electricity prices and gas prices can be explained by the similarity of the market design across Europe and by the same marginal generation technology. Since standard unit root and cointegration tests are not robust to the peculiar characteristics of electricity prices time series, we also develop a battery of robust inference procedures that should assure the reliability of our results. Copyright © 2009 John Wiley & Sons, Ltd.     

Improving Electricity Market Price Forecasting with Factor Models for the Optimal Generation Bid

In liberalized electricity markets, the electricity generation companies usually manage their production by developing hourly bids that are sent to the day‐ahead market. As the prices at which the energy will be purchased are unknown until the end of the bidding process, forecasting of spot prices has become an essential element in electricity management strategies. In this article, we apply forecasting factor models to the market framework in Spain and Portugal and study their performance. Although their goodness of fit is similar to that of autoregressive integrated moving average models, they are easier to implement. The second part of the paper uses the spot‐price forecasting model to generate inputs for a stochastic programming model, which is then used to determine the company's optimal generation bid. The resulting optimal bidding curves are presented and analyzed in the context of the Iberian day‐ahead electricity market.     

Forecasting using a periodic transfer function: with an application to the UK price of ferrous scrap

The familiar concept of cointegration enables us to determine whether or not there is a long-run relationship between two integrated time series. However, this may not capture short-run effects such as seasonality. Two series which display different seasonal effects can still be cointegrated. Seasonality may arise independently of the long-run relationship between two time series or, indeed, the long-run relationship may itself be seasonal. The market for recycled ferrous scrap displays these features: the US and UK scrap prices are cointegrated, yet the local markets exhibit different forms of seasonality. The paper addresses the problem of using both cointegrating and seasonal relationships in forecasting time series through the use of periodic transfer function models. We consider the problems of testing for cointegration between series with differing seasonal patterns and develop a periodic transfer function model for the US and UK scrap markets. Forecast comparisons with other time series models suggest that forecasting efficiency may be improved by allowing for periodicity but that such improvement is by no means guaranteed. The correct specification of the periodic component of the model is critical for forecast accuracy.     

Housing market dynamics: Evidence of mean reversion and downward rigidity

House prices often exhibit serial correlation and mean reversion. Using two large panel datasets, this paper analyzes the price dynamics in two significantly different types of markets, cyclical (or volatile) and non-cyclical (or tame), by applying an autoregressive mean reversion (ARMR) model. Our results show that cyclical markets have larger AR coefficients than non-cyclical markets. As a result, house prices in cyclical markets tend to have larger price cycles. We also find that the upward periods have larger AR coefficients than the downward periods. This demonstrates that house prices are likely to overshoot the equilibrium in appreciating markets while experiencing downward rigidity during periods of decline. The model developed in this paper can produce a forecast with rich house price dynamics across markets. Our results can also be used to determine how house prices in overvalued markets will ultimately adjust.     

A reduced form framework for modeling volatility of speculative prices based on realized variation measures

Building on realized variance and bipower variation measures constructed from high-frequency financial prices, we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility. We decompose the total daily return variability into the continuous sample path variance, the variation arising from discontinuous jumps that occur during the trading day, as well as the overnight return variance. Our empirical results, based on long samples of high-frequency equity and bond futures returns, suggest that the dynamic dependencies in the daily continuous sample path variability are well described by an approximate long-memory HAR–GARCH model, while the overnight returns may be modeled by an augmented GARCH type structure. The dynamic dependencies in the non-parametrically identified significant jumps appear to be well described by the combination of an ACH model for the time-varying jump intensities coupled with a relatively simple log-linear structure for the jump sizes. Finally, we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out-of-sample forecasts for the total return volatility.     

Partially overlapping time series: a new model for volatility dynamics in commodity futures

In commodity futures markets, contracts with various delivery dates trade simultaneously. Applied researchers typically discard the majority of the data and form a single time series by choosing only one price observation per day. This strategy precludes a full understanding of these markets and can induce complicated nonlinear dynamics in the data. In this paper, I introduce the partially overlapping time series (POTS) model to model jointly all traded contracts. The POTS model incorporates time‐to‐delivery, storability, seasonality and GARCH effects. I apply the POTS model to corn futures at the Chicago Board of Trade and the results uncover substantial inefficiency associated with delivery on corn futures. The results also support two theories of commodity pricing: the theory of storage and the Samuelson effect. Copyright © 2005 John Wiley & Sons, Ltd.     

Structural breaks and GARCH models of exchange rate volatility

We investigate the empirical relevance of structural breaks for GARCH models of exchange rate volatility using both in‐sample and out‐of‐sample tests. We find significant evidence of structural breaks in the unconditional variance of seven of eight US dollar exchange rate return series over the 1980–2005 period—implying unstable GARCH processes for these exchange rates—and GARCH(1,1) parameter estimates often vary substantially across the subsamples defined by the structural breaks. We also find that it almost always pays to allow for structural breaks when forecasting exchange rate return volatility in real time. Combining forecasts from different models that accommodate structural breaks in volatility in various ways appears to offer a reliable method for improving volatility forecast accuracy given the uncertainty surrounding the timing and size of the structural breaks. Copyright © 2008 John Wiley & Sons, Ltd.     

ECONOMETRIC MODELS OF ASYMMETRIC PRICE TRANSMISSION

Abstract In this paper, we review the existing empirical literature on price asymmetries in commodities, providing a way to classify and compare different studies that are highly heterogeneous in terms of econometric models, type of asymmetries and empirical findings. Relative to the previous literature, this paper is novel in several respects. First, it presents a detailed and updated survey of the existing empirical contributions on price asymmetries in the transmission mechanism linking input prices to output prices. Second, this paper presents an extension of the traditional distinction between long‐run and short‐run asymmetries to new categories of asymmetries, such as: contemporaneous impact, distributed lag effect, cumulated impact, reaction time, equilibrium and momentum equilibrium adjustment path, regime effect, regime equilibrium adjustment path. Each empirical study is then critically discussed in the light of this new classification of asymmetries. Third, this paper evaluates the relative merits of the most popular econometric models for price asymmetries, namely autoregressive distributed lags, partial adjustments, error correction models, regime switching and vector autoregressive models. Finally, we use the meta‐regression analysis to investigate whether the results of asymmetry tests are not model‐invariant and find which additional factors systematically influence the rejection of the null hypothesis of symmetric price adjustment. The main results of our survey can be summarized as follows: (i) each econometric model is specialized to capture a subset of asymmetries; (ii) each asymmetry is better investigated by a subset of econometric models; (iii) the general significance of the F test for asymmetric price transmission depends mainly on characteristics of the data, dynamic specification of the econometric model, and market characteristics. Overall, our empirical findings confirm that asymmetry, in all its forms, is very likely to occur in a wide range of markets and econometric models.     

The behavior of speculative prices and the consistency of economic models

Modern financial economic theory suggest that changes in speculative prices should follow simple ‘fair game’ processes in an informationally efficient capital market. The observation that changes in speculative prices follow simple time series processes both supports this theoretical proposition and suggest restrictions on the transfer functions of structural econometric models in which speculative prices appear as output variables. The simplicity of the time series processes for observed changes in speculative prices are shown to impose strong restrictions on potential equilibrium models of asset pricing, informational disequilibrium models of financial markets, and many monetary and macroeconomic models as well.     

Commodity-price volatility and macroeconomic spillovers: Evidence from nine emerging markets

The recent decade has witnessed wild swings in global commodity prices, with large increases preceding the Global Financial Crisis and steep declines following the crash. Many emerging markets find themselves destabilized by these fluctuations, not only when price increases lead to currency appreciations and reduced competitiveness, but also when price decreases cause capital outflows and deteriorations in the balance of payments. This study examines the volatility processes of six major commodity prices, before applying Multivariate GARCH analysis to examine spillovers among important commodity prices and output, exchange rates, interest rates and inflation in major emerging markets. While each commodity and each country behaves differently, we find that Chile is most closely tied to the copper price, and Indonesia to oil and tin, while neighbors such as Brazil and the Philippines are less affected. Perhaps surprisingly, Russia is found to be highly insulated from fluctuations in world oil prices.     

Probabilistic forecasting in day-ahead electricity markets: Simulating peak and off-peak prices

In this article we include dependency structures for electricity price forecasting and forecasting evaluation. We work with off-peak and peak time series from the German-Austrian day-ahead price; hence, we analyze bivariate data. We first estimate the mean of the two time series, and then in a second step we estimate the residuals. The mean equation is estimated by ordinary least squares and the elastic net, and the residuals are estimated by maximum likelihood. Our contribution is to include a bivariate jump component in a mean reverting jump diffusion model in the residuals. The models’ forecasts are evaluated with use of four different criteria, including the energy score to measure whether the correlation structure between the time series is properly included. It is observed that the models with bivariate jumps provide better results with the energy score, which means that it is important to consider this structure to properly forecast correlated time series.     

Prediction market prices under risk aversion and heterogeneous beliefs

In this paper, we examine the properties of prediction market prices when risk averse traders have heterogeneous beliefs in state probabilities. We show that the equilibrium state prices equal the mean beliefs of traders about that state if and only if the traders’ common utility function is logarithmic. We also provide a necessary and sufficient condition ensuring that the state prices are systematically below or above the mean beliefs of traders, thus providing a rational explanation to the favorite-longshot bias in prediction markets.     

Trading constraints penalizing default: A recursive approach

This paper proves existence of an ergodic Markov equilibrium for a class of general equilibrium economies with infinite horizon, incomplete markets, and default. Agents may choose to deny their liabilities and face trading constraints that depend on the adjusted amount of past default on each asset. These constraints replace the usual utility penalties and explore intertemporal tie-ins that appear in dynamic economies. The equilibrium prices and solvency rates present stationary properties that are usually required in econometric models of credit risk.     

Optimal Control of Heteroscedastic Macroeconomic Models

This paper analyses the implications of heteroscedasticity for optimal macroeconomic policy and welfare. We find that changes in the variance structure driven by exogenous processes like generalized autoregressive conditional heteroscedasticity (GARCH) affect welfare but not the optimal feedback rule. However, changes in the variance structure driven by state‐dependent processes affect both. We also derive certainty‐equivalent transformations of state‐dependent volatility models that allow standard quadratic dynamic programming algorithms to be employed to study optimal policy. These results are illustrated numerically using a reduced‐form model of the US economy in which changes in volatility are driven by a GARCH process and the rate of inflation. Copyright © 2015 John Wiley & Sons, Ltd.