Estimation of objective and risk-neutral distributions based on moments of integrated volatility

In this paper, we present an estimation procedure which uses both option prices and high-frequency spot price feeds to estimate jointly the objective and risk-neutral parameters of stochastic volatility models. The procedure is based on a method of moments that uses analytical expressions for the moments of the integrated volatility and series expansions of option prices and implied volatilities. This results in an easily implementable and rapid estimation technique. An extensive Monte Carlo study compares various procedures and shows the efficiency of our approach. Empirical applications to the Deutsche mark–US dollar exchange rate futures and the S&P 500 index provide evidence that the method delivers results that are in line with the ones obtained in previous studies where much more involved estimation procedures were used.     

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.     

Exchange rates and oil prices: A multivariate stochastic volatility analysis

This paper uses the multivariate stochastic volatility (MSV) and the multivariate GARCH (MGARCH) models to investigate the volatility interactions between the oil market and the foreign exchange (FX) market, in an attempt to extract information intertwined in the two for better volatility forecast. Our analysis takes into account structural breaks in the data. We find that when the markets are relatively calm (before the 2008 crisis), both oil and FX markets respond to shocks simultaneously and therefore no interaction is detected in daily data. However, during turbulent time, there is bi-directional volatility interaction between the two. In other words, innovations that hit one market also have some impact on the other at a later date and thus using such a dependence significantly improves the forecasting power of volatility models. The MSV models outperform others in fitting the data and forecasting exchange rate volatility. However, the MGARCH models do better job in forecasting oil volatility.     

The exchange rate pass-through in the new EU member states

This paper aims to complete our understanding of the relationship between changes in nominal effective exchange rates and prices in the new EU member states. I investigate the exchange rate pass-through to import, producer and consumer prices for ten Central and Eastern European countries with quarterly data from January 1996 to December 2011. In a first step, the pass-through estimates are derived from a dynamic panel data model through the generalized method of moments. A statistically significant exchange rate pass-through to consumer, producer and import prices is found, both in the short and long run. In a second step, I proceed to an individual analysis, country by country, and find support for an increased heterogeneity in the exchange rate pass-through estimates. In a third step, I assess the drivers of the estimated exchange rate pass-through coefficients and find support for a significant impact of exchange rate volatility, inflation volatility, import dependence, and the output gap, as well as the global outlook.     

A non-linear filtering approach to stochastic volatility models with an application to daily stock returns

This paper develops a new model for the analysis of stochastic volatility (SV) models. Since volatility is a latent variable in SV models, it is difficult to evaluate the exact likelihood. In this paper, a non-linear filter which yields the exact likelihood of SV models is employed. Solving a series of integrals in this filter by piecewise linear approximations with randomly chosen nodes produces the likelihood, which is maximized to obtain estimates of the SV parameters. A smoothing algorithm for volatility estimation is also constructed. Monte Carlo experiments show that the method performs well with respect to both parameter estimates and volatility estimates. We illustrate our model by analysing daily stock returns on the Tokyo Stock Exchange. Since the method can be applied to more general models, the SV model is extended so that several characteristics of daily stock returns are allowed, and this more general model is also estimated. Copyright © 1999 John Wiley & Sons, Ltd.     

Forecasting stock prices with commodity prices: New evidence from Feasible Quasi Generalized Least Squares (FQGLS) with non-linearities

The complexities in modern stock markets make it imperative to unravel the possible predictors of their future values. This paper thus provides insights into the predictability of stock prices of the BRICS countries with large dependence on commodities either for foreign exchange earnings or industrial while accounting for the role of asymmetries. Essentially, empirical evidence abound for the high volatility in world commodity markets, thus making us to determine if positive and negative changes in commodity prices predict stock prices differently. In addition, unlike the traditional forecast models, our choice of forecast models additionally addresses certain statistical features, including conditional heteroskedasticity, serial dependence, persistence and endogeneity, inherent in the predictors, which have the potential of causing estimation bias. In all, we find evidence in favour of the ability of commodity prices to predict stock prices of Brazil, Russia and South Africa. Also, both the in-sample and out-of-sample forecast performances of the predicted models support asymmetries in a number of commodity prices in each of these three countries. Our results are robust to different data samples and forecast horizons.     

Calibration of stochastic volatility models: A Tikhonov regularization approach

We aim to calibrate stochastic volatility models from option prices. We develop a Tikhonov regularization approach with an efficient numerical algorithm to recover the risk neutral drift term of the volatility (or variance) process. In contrast to most existing literature, we do not assume that the drift term has any special structure. As such, our algorithm applies to calibration of general stochastic volatility models. An extensive numerical analysis is presented to demonstrate the efficiency of our approach. Interestingly, our empirical study reveals that the risk neutral variance processes recovered from market prices of options on S&P 500 index and EUR/USD exchange rate are indeed linearly mean-reverting.     

Causality and volatility patterns between gold prices and exchange rates

This paper provides a new perspective on the link between gold prices and exchange rates. Based on gold prices denominated in five different currencies and the related bilateral exchange rates, we put causalities and short-run volatility transmission under closer scrutiny. We provide evidence that the identification of a strong hedge function of gold requires an explicit modeling of the volatility component. For all currencies, exchange rate depreciations initially have a negative impact on the gold price after one day which turns out to be positive after two days in most of the cases. Contrary to previous studies, our results point to a specific role of the dollar in the context of gold-exchange rate relationships: volatility of dollar exchange rates more frequently results in strong hedging functions of gold prices. Furthermore, the gold price denominated in the US dollar tends to increase after a depreciation of the dollar.     

Forecasting exchange rate volatility using high-frequency data: Is the euro different?

We assess the performances of alternative procedures for forecasting the daily volatility of the euro’s bilateral exchange rates using 15 min data. We use realized volatility and traditional time series volatility models. Our results indicate that using high-frequency data and considering their long memory dimension enhances the performance of volatility forecasts significantly. We find that the intraday FIGARCH model and the ARFIMA model outperform other traditional models for all exchange rate series.     

Do interest rate options contain information about excess returns?

There is strong empirical evidence that long-term interest rates contain a time-varying risk premium. Options may contain valuable information about this risk premium because their prices are sensitive to the underlying interest rates. We use the joint time series of swap rates and interest rate option prices to estimate dynamic term structure models. The risk premiums that we estimate using option prices are better able to predict excess returns for long-term swaps over short-term swaps. Moreover, in contrast to the previous literature, the most successful models for predicting excess returns have risk factors with stochastic volatility. We also show that the stochastic volatility models we estimate using option prices match the failure of the expectations hypothesis.     

Testing the Information Structure of Eastern European Markets: The Warsaw Stock Exchange

This paper investigates the content of the information set used by the agents in the Warsaw Stock Exchange - WSE. Three “candidate variables” are examined — consumers’ prices, the zloty/US$ exchange rate and the refinancing rate of the National Bank of Poland — with respect to three WSE stocks, from different sectors of the economy. The methodology employed supposes that the innovations in the price series are orthogonal to all variables within or outside the information set. Beyond the question of how to specify the agents expectations, the WSE trading rules and the high volatility period present in all monthly price series were additional problems to render it operational. Given the solutions adopted, in only three out of the nine cases tested, it was possible to reject the null that the candidate did not belong to the information set. This is a signal that macroeconomic fundamentals are still absent from the WSE. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cointegration tests of present value models with a time-varying discount factor

The paper analyses the impact of persistence and volatility in the discount rate in present-value models on cointegration tests in levels and in logarithms. In simulations we find that the probability of not rejecting the null of no cointegration depends on the persistence of the discount rate process and can be very high when the expected returns process is highly persistent. In contrast, the cointegration tests are very robust with respect to the level of volatility in the discount rate. We discuss the relevance of our findings for the US stock market where standard ADF tests do not reject the null of no cointegration between stock prices and dividends. Based on estimates of persistence in four asset pricing models, we find that a model which links expected returns to the dividend yield is sufficiently persistent to explain the failure of rejecting the null that stock prices and dividends are not cointegrated.     

An objective function for simulation based inference on exchange rate data

The assessment of models of financial market behaviour requires evaluation tools. When complexity hinders a direct estimation approach, e.g., for agent based microsimulation models, simulation based estimators might provide an alternative. In order to apply such techniques, an objective function is required, which should be based on robust statistics of the time series under consideration. Based on the identification of robust statistics of foreign exchange rate time series in previous research, an objective function is derived. This function takes into account stylized facts about the unconditional distribution of exchange rate returns and properties of the conditional distribution, in particular, autoregressive conditional heteroscedasticity and long memory. A bootstrap procedure is used to obtain an estimate of the variance-covariance matrix of the different moments included in the objective function, which is used as a base for the weighting matrix. Finally, the properties of the objective function are analyzed for two different agent based models of the foreign exchange market, a simple GARCH-model and a stochastic volatility model using the DM/US-$ exchange rate as a benchmark. It is also discussed how the results might be used for inference purposes. Research has been supported by the DFG grant WI 20024/2-1/2. We are indebted to two anonymous referees of this journal, Leigh Tesfatsion, Patrick Burns and other participants of the CEF’06 conference in Limassol for helpful comments on preliminary versions of this paper.     

Impact of an unexplained component of real exchange rate volatility on FDI: Evidence from transition countries

The aim of this paper is to examine the impact of an unexplained component of real exchange rate volatility on FDI in transition economies. We make an attempt to overcome some problems associated with previous studies; the aggregation problem, inadequate measures of volatility, short-run focus and the endogeneity problem. Using a GARCH specification, we focus on long-run volatility, while we control for the endogeneity problem by applying SYS-GMM estimation. The obtained results show that the impact of the unexplained component of real exchange rate volatility on FDI differs among economic activities since 2000. As part of the re-estimation exercise, we use two alternative measures of volatility to avoid arbitrariness. The obtained results are to a large extent in accordance with the first one.     

An application of nonparametric volatility estimators to option pricing

We discuss the impact of volatility estimates from high frequency data on derivative pricing. The principal purpose is to estimate the diffusion coefficient of an Itô process using a nonparametric Nadaraya–Watson kernel approach based on selective estimators of spot volatility proposed in the econometric literature, which are based on high frequency data. The accuracy of different spot volatility estimates is measured in terms of how accurately they can reproduce market option prices. To this aim, we fit a diffusion model to S&P 500 data, and successively, we use the calibrated model to price European call options written on the S&P 500 index. The estimation results are compared to well-known parametric alternatives available in the literature. Empirical results not only show that using intra-day data rather than daily provides better volatility estimates and hence smaller pricing errors, but also highlight that the choice of the spot volatility estimator has effective impact on pricing.     

Forecasting realized volatility: a Bayesian model‐averaging approach

How to measure and model volatility is an important issue in finance. Recent research uses high‐frequency intraday data to construct ex post measures of daily volatility. This paper uses a Bayesian model‐averaging approach to forecast realized volatility. Candidate models include autoregressive and heterogeneous autoregressive specifications based on the logarithm of realized volatility, realized power variation, realized bipower variation, a jump and an asymmetric term. Applied to equity and exchange rate volatility over several forecast horizons, Bayesian model averaging provides very competitive density forecasts and modest improvements in point forecasts compared to benchmark models. We discuss the reasons for this, including the importance of using realized power variation as a predictor. Bayesian model averaging provides further improvements to density forecasts when we move away from linear models and average over specifications that allow for GARCH effects in the innovations to log‐volatility. Copyright © 2009 John Wiley & Sons, Ltd.     

An assessment of another decade of capital controls in Colombia: 1998–2008

We explore the effectiveness of capital controls in Colombia. We analyze the impact of administrative restrictions to capital flows on aggregate capital flows, the composition of capital flows, the real exchange rate, and economic activity using restricted versions of vector error correction models (VEC) that control for exogenous global financial conditions. The models are estimated using monthly data ranging from August of 1998 to May of 2008. In addition we estimate GARCH models to identify if capital controls have had relevant impacts on the volatility of the nominal exchange rate and of other relevant asset prices. These models are estimated using weekly data covering the same time period. Results suggest that the capital controls used since 1998 have been ineffective in reducing capital flows and the trend of the Colombian peso to appreciate. In addition there is no evidence suggesting a change in the composition of capital flows induced by capital controls. We find some evidence in favor of capital controls reducing nominal exchange rate volatility at high frequencies.     

基于极值分布理论的VaR与ES度量

本文应用极值分布理论对金融收益序列的尾部进行估计,计算收益序列的在险价值VaR和预期不足ES来度量市场风险。通过伪最大似然估计方法估计的GARCH模型对收益数据进行拟合,应用极值理论中的GPD对新息分布的尾部建模,得到了基于尾部估计产生收益序列的VaR和ES值。采用上证指数日对数收益数据为样本,得到了度量条件极值和无条件极值下VaR和ES的结果。实证研究表明:在置信水平很高(如99%)的条件下,采用极值方法度量风险值效果更好。而置信水平在95%下,其他方法和极值方法结合效果会很好。用ES度量风险能够使我们了解不利情况发生时风险的可能情况。     

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.