Using an Euler discretization to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative, the discretization is not. Although an ...exact and efficient simulation algorithm exists for this process, at present this is not the case for the CEV-SV stochastic volatility model, with the Heston model as a special case, where the variance is modelled as a mean-reverting CEV process. Consequently, when using an Euler discretization, one must carefully think about how to fix negative variances. Our contribution is threefold. Firstly, we unify all Euler fixes into a single general framework. Secondly, we introduce the new full truncation scheme, tailored to minimize the positive bias found when pricing European options. Thirdly and finally, we numerically compare all Euler fixes to recent quasi-second order schemes of Kahl and Jäckel, and Ninomiya and Victoir, as well as to the exact scheme of Broadie and Kaya. The choice of fix is found to be extremely important. The full truncation scheme outperforms all considered biased schemes in terms of bias and root-mean-squared error.
Realized variance, being the summation of squared intra-day returns, has quickly gained popularity as a measure of daily volatility. Following Parkinson 1980. The extreme value method for estimating ...the variance of the rate of return. Journal of Business 53, 61–65 we replace each squared intra-day return by the high–low range for that period to create a novel and more efficient estimator called the realized range. In addition, we suggest a bias-correction procedure to account for the effects of microstructure frictions based upon scaling the realized range with the average level of the daily range. Simulation experiments demonstrate that for plausible levels of non-trading and bid–ask bounce the realized range has a lower mean-squared error than the realized variance, including variants thereof that are robust to microstructure noise. Empirical analysis of the S&P500 index-futures and the S&P100 constituents confirms the potential of the realized range.
•Trading speed is crucially important for high-frequency trading based on U.S. macroeconomic news.•Annual losses due to being slow with 300ms (1second) can accumulate to 1.94% (3.90%.•The effect of ...algorithmic trading on market quality depends on the type of algorithm active.•Algorithmic activity increases depth at the best quotes, but decreases overall depth.•Algorithmic activity following a macroeconomic news arrival increases volatility.
This paper documents that speed is crucially important for high-frequency trading strategies based on U.S. macroeconomic news releases. Using order-level data on the highly liquid S&P 500 ETF traded on NASDAQ from January 6, 2009 to December 12, 2011, we find that a delay of 300ms or more significantly reduces returns of news-based trading strategies. This reduction is greater for high impact news and on days with high volatility. In addition, we assess the effect of algorithmic trading on market quality around macroeconomic news. In the minute following a macroeconomic news arrival, algorithmic activity increases trading volume and depth at the best quotes, but also increases volatility and leads to a drop in overall depth. Quoted half-spreads decrease (increase) when we measure algorithmic trading over the full (top of the) order book.
We test for a change in the volatility of 214 U.S. macroeconomic time series over the period 1959-1999. We find that approximately 80% of these series have experienced a break in unconditional ...volatility during this period. Even though more than half of the series experienced a break in conditional mean, most of the reduction in volatility appears to be due to changes in conditional volatility. Our results are robust to controlling for business cycle nonlinearity in both mean and variance. Volatility changes are more appropriately characterized as instantaneous breaks than as gradual changes. Nominal variables such as inflation and interest rates experienced multiple volatility breaks and witnessed temporary increases in volatility during the 1970s. On this evidence, we conclude that the increased stability of economic fluctuations is widespread.
The dynamic factor Markov-switching (DFMS) model introduced by Diebold and Rudebusch (1996) has proven to be a powerful framework for measuring the business cycle. We extend the DFMS model by ...allowing for time-varying transition probabilities, intending to accelerate the real-time dating of business cycle peaks. Time-variation of the transition probabilities is brought about endogenously using the score-driven approach and exogenously using the term spread. In a real-time application using the four components of The Conference Board’s Coincident Economic Index for 1959–2020, we find that signaling power for recessions is significantly improved. We are able to date the 2001 and 2008 recession peaks four and two months after the peak date, which is four and ten months before the NBER.
The daily average price of electricity represents the price of electricity to be delivered over the full next day and serves as a key reference price in the electricity market. It is an aggregate ...that equals the average of hourly prices for delivery during each of the 24 individual hours. This paper demonstrates that the disaggregated hourly prices contain useful predictive information for the daily average price in the Nord Pool market. Multivariate models for the full panel of hourly prices significantly outperform univariate models of the daily average price, with reductions in Root Mean Squared Error of up to 16%. Substantial care is required in order to achieve these forecast improvements. Rich multivariate models are needed to exploit the relations between different hourly prices, but the risk of overfitting must be mitigated by using dimension reduction techniques, shrinkage and forecast combinations.
•We demonstrate that disaggregated hourly prices contain predictive information for the daily average price.•Results for the average daily electricity price as well as for individual hourly prices are reported and evaluated.•Multivariate models for the full panel of hourly prices outperform univariate models of the daily average price.•Improvement is accomplished using dimension reduction and shrinkage techniques which mitigate overfitting.•Forecast Combination techniques grant further improvement.
This paper shows that stock market contagion occurs as a domino effect, where confined local crashes evolve into more widespread crashes. Using a novel framework based on ordered logit regressions we ...model the occurrence of local, regional and global crashes as a function of their past occurrences and financial variables. We find significant evidence that global crashes do not occur abruptly but are preceded by local and regional crashes. Besides this form of contagion, interdependence shows up by the effect of interest rates, bond returns and stock market volatility on crash probabilities. When it comes to forecasting global crashes, our model outperforms a binomial model for global crashes only.
Abstract
We investigate the effect of estimation error on backtests of expected shortfall (ES) forecasts. These backtests are based on first-order conditions of a recently introduced family of ...jointly consistent loss functions for value-at-risk (VaR) and ES. For both single and multiperiod horizons, we provide explicit expressions for the additional terms in the asymptotic covariance matrix that result from estimation error, and propose robust tests that account for it. Monte Carlo experiments show that the tests that ignore these terms suffer from size distortions, which are more pronounced for higher ratios of out-of-sample to in-sample observations. Robust versions of the backtests perform well with power against common alternatives. We also introduce a novel standardization of the conditional joint test statistic that removes the need to estimate higher-order moments and significantly improves its performance. In an application to VaR and ES forecasts for daily FTSE 100 index returns as generated by (GJR-)GARCH and HEAVY models, we find that estimation error substantially impacts the outcome of the backtests, and is not bound to particular subperiods such as the credit crisis.
We develop a new score-driven model for the joint dynamics of fat-tailed realized covariance matrix observations and daily returns. The score dynamics for the unobserved true covariance matrix are ...robust to outliers and incidental large observations in both types of data by assuming a matrix-F distribution for the realized covariance measures and a multivariate Student's t distribution for the daily returns. The filter for the unknown covariance matrix has a computationally efficient matrix formulation, which proves beneficial for estimation and simulation purposes. We formulate parameter restrictions for stationarity and positive definiteness. Our simulation study shows that the new model is able to deal with high-dimensional settings (50 or more) and captures unobserved volatility dynamics even if the model is misspecified. We provide an empirical application to daily equity returns and realized covariance matrices up to 30 dimensions. The model statistically and economically outperforms competing multivariate volatility models out-of-sample. Supplementary materials for this article are available online.
We evaluate the forecasting performance of time series models for realized volatility, which accommodate long memory, level shifts, leverage effects, day-of-the-week and holiday effects, as well as ...macroeconomic news announcements. Applying the models to daily realized volatility for the S&P 500 futures index, we find that explicitly accounting for these stylized facts of volatility improves out-of-sample forecast accuracy for horizons up to 20 days ahead. Capturing the long memory feature of realized volatility by means of a flexible high-order AR-approximation instead of a parsimonious but stringent fractionally integrated specification also leads to improvements in forecast accuracy, especially for longer horizon forecasts.
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