Dynamic Asymmetric GARCH

This article develops the dynamic asymmetric GARCH (or DAGARCH)model that generalizes asymmetric GARCH models such as thatof Glosten, Jagannathan, and Runkle (GJR), introduces multiplethresholds, and makes the asymmetric effect time dependent.We provide the stationarity conditions for the DAGARCH modeland show how GJR can be obtained as a special case. Furthermore,we derive the news impact curve implied by the DAGARCH modeland demonstrate its flexibility. An application to daily stockmarket indices is presented to demonstrate the practical usefulnessof the new model.     

On the distribution and conditional heteroscedasticity in Taiwan stock prices

This paper studies the distribution and conditional heteroscedasticity in stock returns on the Taiwan stock market. Apart from the normal distribution, in order to explain the leptokurtosis and skewness observed in the stock return distribution, we also examine the Student-t, the Poisson–normal, and the mixed-normal distributions, which are essentially a mixture of normal distributions, as conditional distributions in the stock return process. We also use the ARMA (1,1) model to adjust the serial correlation, and adopt the GJR–generalized autoregressive conditional heteroscedasticity (GARCH (1,1)) model to account for the conditional heterscedasticity in the return process. The empirical results show that the mixed–normal–GARCH model is the most probable specification for Taiwan stock returns. The results also show that skewness seems to be diversifiable through portfolio. Thus the normal–GARCH or the Student-t–GARCH model which involves symmetric conditional distribution may be a reasonable model to describe the stock portfolio return process¹.     

Intraday Return Volatility Process: Evidence from NASDAQ Stocks

This paper presents a comprehensive analysis of the distributional and time-series properties of intraday returns. The purpose is to determine whether a GARCH model that allows for time varying variance in a process can adequately represent intraday return volatility. Our primary data set consists of 5-minute returns, trading volumes, and bid-ask spreads during the period January 1, 1999 through March 31, 1999, for a subset of thirty stocks from the NASDAQ 100 Index. Our results indicate that the GARCH(1,1) model best describes the volatility of intraday returns. Current volatility can be explained by past volatility that tends to persist over time. These results are consistent with those of Akgiray (1989) who estimates volatility using the various ARCH and GARCH specifications and finds the GARCH(1,1) model performs the best. We add volume as an additional explanatory variable in the GARCH model to examine if volume can capture the GARCH effects. Consistent with results of Najand and Yung (1991) and Foster (1995) and contrary to those of Lamoureux and Lastrapes (1990), our results show that the persistence in volatility remains in intraday return series even after volume is included in the model as an explanatory variable. We then substitute bid-ask spread for volume in the conditional volatility equation to examine if the latter can capture the GARCH effects. The results show that the GARCH effects remain strongly significant for many of the securities after the introduction of bid-ask spread. Consistent with results of Antoniou, Homes and Priestley (1998), intraday returns also exhibit significant asymmetric responses of volatility to flow of information into the market.     

The threshold effect in expected volatility: a model based on asymmetric information

This article develops theoretical insight into the thresholdeffect in expected volatility, which means that large shocksare less persistent in volatility than small shocks. The modeluses the Kyle-Admati-Pfleiderer setup with liquidity traders,informed traders, and a market maker. Information is modeledas a GARCH process. It is shown that the GARCH process for informationis transformed into a TARCH process (for 'threshold GARCH')for the market price changes. Working with information flowsallows one to derive implications for trading volume and marketliquidity which provide the basis for a more complete test ofthe model.     

Robust outlier detection for Asia–Pacific stock index returns

Outliers can lead to model misspecifications, poor forecasts and invalid inferences. Their identification and correction is therefore an important objective of financial modeling.This paper introduces a simple method to detect outliers in a financial series. It uses an AR(1)–GARCH(1,1) model to calculate interval forecasts for one-step ahead returns that are then compared to realized returns to determine whether or not we are in the presence of an aberrant observation. The GARCH model, however, is only used as a filter and the identification algorithm remains robust to model misspecifications.The efficiency of this outlier-correction technique is first tested with a simulation study, before being applied to five Asian stock market returns to identify the outlying observations. After an analysis of these extreme fluctuations, the out-of-sample forecasting performance of our outlier-corrected model is then compared to the classical forecasts of a GARCH model in which no account is taken of outliers.     

Empirical Study of Nikkei 225 Options with the Markov Switching GARCH Model

This paper investigates the pricing of Nikkei 225 Options using the Markov Switching GARCH (MSGARCH) model, and examines its practical usefulness in option markets. We assume that investors are risk-neutral and then compute option prices by using Monte Carlo simulation. The results reveal that, for call options, the MSGARCH model with Student’s t-distribution gives more accurate pricing results than GARCH models and the Black–Scholes model. However, this model does not have good performance for put options.     

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.     

A closed-form GARCH option valuation model

This paper develops a closed-form option valuation formula fora spot asset whose variance follows a GARCH(p, q) process thatcan be correlated with the returns of the spot asset. It providesthe first readily computed option formula for a random volatilitymodel that can be estimated and implemented solely on the basisof observables. The single lag version of this model containsHeston's (1993) stochastic volatility model as a continuous-timelimit. Empirical analysis on S&P500 index options showsthat the out-of-sample valuation errors from the single lagversion of the GARCH model are substantially lower than thead hoc Black-Scholes model of Dumas, Fleming and Whaley (1998)that uses a separate implied volatility for each option to fitto the smirk/smile in implied volatilities. The GARCH modelremains superior even though the parameters of the GARCH modelare held constant and volatility is filtered from the historyof asset prices while the ad hoc Black-Scholes model is updatedevery period. The improvement is largely due to the abilityof the GARCH model to simultaneously capture the correlationof volatility, with spot returns and the path dependence involatility.     

Multivariate term structure models with level and heteroskedasticity effects

The paper introduces and estimates a multivariate level-GARCH model for the long rate and the term-structure spread where the conditional volatility is proportional to the γth power of the variable itself (level effects) and the conditional covariance matrix evolves according to a multivariate GARCH process (heteroskedasticity effects). The long-rate variance exhibits heteroskedasticity effects and level effects in accordance with the square-root model. The spread variance exhibits heteroskedasticity effects but no level effects. The level-GARCH model is preferred above the GARCH model and the level model. GARCH effects are more important than level effects. The results are robust to the maturity of the interest rates.     

A lattice model for option pricing under GARCH-jump processes

This study extends the GARCH pricing tree in Ritchken and Trevor (J Financ 54:366–402, 1999) by incorporating an additional jump process to develop a lattice model to value options. The GARCH-jump model can capture the behavior of asset prices more appropriately given its consistency with abundant empirical findings that discontinuities in the sample path of financial asset prices still being found even allowing for autoregressive conditional heteroskedasticity. With our lattice model, it shows that both the GARCH and jump effects in the GARCH-jump model are negative for near-the-money options, while positive for in-the-money and out-of-the-money options. In addition, even when the GARCH model is considered, the jump process impedes the early exercise and thus reduces the percentage of the early exercise premium of American options, particularly for shorter-term horizons. Moreover, the interaction between the GARCH and jump processes can raise the percentage proportions of the early exercise premiums for shorter-term horizons, whereas this effect weakens when the time to maturity increases.     

NONLINEAR DYNAMICS AND THE DISTRIBUTION OF DAILY STOCK INDEX RETURNS

Three alternative models of daily stock index returns are considered: (1) a diffusion-jump process; (2) an extended generalized autoregressive conditional heteroskedasticity (GARCH) process; and (3) a combination of the GARCH and jump processes. Non-nested tests between the diffusion-jump process and a GARCH(1.1) process with t-distributed errors reject the diffusion-jump process, but do not always reject the GARCH process. Kolmogorov-Smirnov tests of fit, however, reject the GARCH(1,1)-t process for all cases. Nonlinear dependence is not removed for the value-weighted index and the S&P 500 stock index; therefore, deterministic chaos cannot be dismissed.     

Forecasting the weekly time-varying beta of UK firms: GARCH models vs. Kalman filter method

This paper investigates the forecasting ability of three different Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models and the Kalman filter method. The three GARCH models applied are: bivariate GARCH, BEKK GARCH, and GARCH-GJR. Forecast errors based on 20 UK company's weekly stock return (based on time-varying beta) forecasts are employed to evaluate the out-of-sample forecasting ability of both the GARCH models and the Kalman method. Measures of forecast errors overwhelmingly support the Kalman filter approach. Among the GARCH models, GJR appears to provide somewhat more accurate forecasts than the two other GARCH models.     

Evaluation of Black-Scholes and GARCH Models Using Currency Call Options Data

This paper empirically examines the performance of Black-Scholes and Garch-M call option pricing models using call options data for British Pounds, Swiss Francs and Japanese Yen. The daily exchange rates exhibit an overwhelming presence of volatility clustering, suggesting that a richer model with ARCH/GARCH effects might have a better fit with actual prices. We perform dominant tests and calculate average percent mean squared errors of model prices. Our findings indicate that the Black-Scholes model outperforms the GARCH models. An implication of this result is that participants in the currency call options market do not seem to price volatility clusters in the underlying process.     

Forecasting the return distribution using high-frequency volatility measures

The aim of this paper is to forecast (out-of-sample) the distribution of financial returns based on realized volatility measures constructed from high-frequency returns. We adopt a semi-parametric model for the distribution by assuming that the return quantiles depend on the realized measures and evaluate the distribution, quantile and interval forecasts of the quantile model in comparison to a benchmark GARCH model. The results suggest that the model outperforms an asymmetric GARCH specification when applied to the S&P 500 futures returns, in particular on the right tail of the distribution. However, the model provides similar accuracy to a GARCH (1, 1) model when the 30-year Treasury bond futures return is considered.     

Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence

The present study compares the performance of the long memory FIGARCH model, with that of the short memory GARCH specification, in the forecasting of multi-period value-at-risk (VaR) and expected shortfall (ES) across 20 stock indices worldwide. The dataset is composed of daily data covering the period from 1989 to 2009. The research addresses the question of whether or not accounting for long memory in the conditional variance specification improves the accuracy of the VaR and ES forecasts produced, particularly for longer time horizons. Accounting for fractional integration in the conditional variance model does not appear to improve the accuracy of the VaR forecasts for the 1-day-ahead, 10-day-ahead and 20-day-ahead forecasting horizons relative to the short memory GARCH specification. Additionally, the results suggest that underestimation of the true VaR figure becomes less prevalent as the forecasting horizon increases. Furthermore, the GARCH model has a lower quadratic loss between actual returns and ES forecasts, for the majority of the indices considered for the 10-day and 20-day forecasting horizons. Therefore, a long memory volatility model compared to a short memory GARCH model does not appear to improve the VaR and ES forecasting accuracy, even for longer forecasting horizons. Finally, the rolling-sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models. Hence, the parameters' time-variant characteristic cannot be entirely due to the news information arrival process of the market; a portion must be due to the FIGARCH modelling process itself.     

Modeling and forecasting stock return volatility using a random level shift model

We consider the estimation of a random level shift model for which the series of interest is the sum of a short-memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a process which is 0 with some probability (1 ? α) and is a random variable with probability α. Our estimation method transforms such a model into a linear state space with mixture of normal innovations, so that an extension of Kalman filter algorithm can be applied. We apply this random level shift model to the logarithm of daily absolute returns for the S&P 500, AMEX, Dow Jones and NASDAQ stock market return indices. Our point estimates imply few level shifts for all series. But once these are taken into account, there is little evidence of serial correlation in the remaining noise and, hence, no evidence of long-memory. Once the estimated shifts are introduced to a standard GARCH model applied to the returns series, any evidence of GARCH effects disappears. We also produce rolling out-of-sample forecasts of squared returns. In most cases, our simple random level shift model clearly outperforms a standard GARCH(1,1) model and, in many cases, it also provides better forecasts than a fractionally integrated GARCH model.     

Regime-switching stochastic volatility and short-term interest rates

In this paper, we introduce regime switching in a two-factor stochastic volatility (SV) model to explain the behavior of short-term interest rates. We model the volatility of short-term interest rates as a stochastic volatility process whose mean is subject to shifts in regime. We estimate the regime-switching stochastic volatility (RSV) model using a Gibbs Sampling-based Markov Chain Monte Carlo algorithm. In-sample results strongly favor the RSV model in comparison to the single-state SV model and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) family of models. Out-of-sample results are mixed and, overall, provide weak support for the RSV model.     

An empirical comparison of GARCH option pricing models

Recent empirical studies have shown that GARCH models can be successfully used to describe option prices. Pricing such contracts requires knowledge of the risk neutral cumulative return distribution. Since the analytical forms of these distributions are generally unknown, computationally intensive numerical schemes are required for pricing to proceed. Heston and Nandi (2000) consider a particular GARCH structure that permits analytical solutions for pricing European options and they provide empirical support for their model. The analytical tractability comes at a potential cost of realism in the underlying GARCH dynamics. In particular, their model falls in the affine family, whereas most GARCH models that have been examined fall in the non-affine family. This article takes a closer look at this model with the objective of establishing whether there is a cost to restricting focus to models in the affine family. We confirm Heston and Nandi's findings, namely that their model can explain a significant portion of the volatility smile. However, we show that a simple non affine NGARCH option model is superior in removing biases from pricing residuals for all moneyness and maturity categories especially for out-the-money contracts. The implications of this finding are examined. JEL Classification G13     

Are RiskMetrics forecasts good enough? Evidence from 31 stock markets

Academic research has highlighted the inherent flaws within the RiskMetrics model and demonstrated the superiority of the GARCH approach in-sample. However, these results do not necessarily extend to forecasting performance. This paper seeks answer to the question of whether RiskMetrics volatility forecasts are adequate in comparison to those obtained from GARCH models. To answer the question stock index data is taken from 31 international markets and subjected to two exercises, a straightforward volatility forecasting exercise and a Value-at-Risk exceptions forecasting competition. Our results provide some simple answers to the above question. When forecasting volatility of the G7 stock markets the APARCH model, in particular, provides superior forecasts that are significantly different from the RiskMetrics models in over half the cases. This result also extends to the European markets with the APARCH model typically preferred. For the Asian markets the RiskMetrics model performs well, and is only significantly dominated by the GARCH models for one market, although there is evidence that the APARCH model provides a better forecast for the larger Asian markets. Regarding the Value-at-Risk exercise, when forecasting the 1% VaR the RiskMetrics model does a poor job and is typically the worst performing model, again the APARCH model does well. However, forecasting the 5% VaR then the RiskMetrics model does provide an adequate performance. In short, the RiskMetrics model only performs well in forecasting the volatility of small emerging markets and for broader VaR measures.