Long-Range Dependence in U.S. Home Price Volatility

The existence of GARCH effects in a financial price series means that the probability of large losses is much higher than standard mean-variance analysis suggests. Accordingly, several recent papers have investigated whether GARCH effects exist in the U.S. housing market, as changes in house prices can have far-ranging impacts on defaults, foreclosures, tax revenues and the values of mortgage-backed securities. Some research in finance indicates that the conditional variance of some assets exhibits far greater persistence, or even “long memory”, than is accounted for in standard GARCH models. If house prices do indeed have this very persistent volatility, properly estimating the conditional variance to allow for such persistence is crucial for optimal portfolio management. We examine a number of U.S. metropolitan areas, and find that, for those with significant GARCH effects, more than half indeed exhibit the very high persistence found in other assets such as equities. We also find that, for those markets exhibiting such persistent volatility, C-GARCH models typically do a better job in forecasting than standard GARCH models. Moreover, there is some tentative evidence that metro areas with the fastest appreciation may be most likely to have such long memory conditional variance. These findings should help in improving risk management, through, for instance the construction of better-specified value-at-risk models.     

VARIANCE,RETURN, AND HIGH-LOW PRICE SPREADS

We report three new findings that rely upon the high-low price range as an estimate of stock return variance. The predictability of variance is associated with persistence in high prices and with correlated shocks to high and low prices. Excess stock returns are positively related to anticipated variance and inversely related to unanticipated variance. Lagged squared residuals in GARCH(1,1) models have no incremental explanatory power in the presence of forecasts of conditional volatility generated from high-low price spread models.     

ANALYSIS OF FEDERAL FUNDS RATE CHANGES AND VARIANCE PATTERNS

We analyze Fed funds rate changes in GARCH‐in‐mean (GARCH‐M) models and find that daily rate change and variance patterns differ with the timing of the rate observation, but that all patterns are generally consistent with optimal reserve account management. We also find that Fed funds daily and intraday variances exhibit trends and persistence, and that daily variance effects differ when using marginal rates versus daily weighted average rates. Furthermore, we find that conditional variances do not provide information about daily or intraday rate changes. Our results provide support for the use of GARCH models for studies on other financial assets. JEL classification: G21, G28     

Model risk of the implied GARCH-normal model

Model risk causes significant losses in financial derivative pricing and hedging. Investors may undertake relatively risky investments due to insufficient hedging or overpaying implied by flawed models. The GARCH model with normal innovations (GARCH-normal) has been adopted to depict the dynamics of the returns in many applications. The implied GARCH-normal model is the one minimizing the mean square error between the market option values and the GARCH-normal option prices. In this study, we investigate the model risk of the implied GARCH-normal model fitted to conditional leptokurtic returns, an important feature of financial data. The risk-neutral GARCH model with conditional leptokurtic innovations is derived by the extended Girsanov principle. The option prices and hedging positions of the conditional leptokurtic GARCH models are obtained by extending the dynamic semiparametric approach of Huang and Guo [Statist. Sin., 2009, 19, 1037–1054]. In the simulation study we find significant model risk of the implied GARCH-normal model in pricing and hedging barrier and lookback options when the underlying dynamics follow a GARCH-t model.     

An analytical approximation to the option formula for the GARCH model

This article derives an analytical approximation to the option formula for a spot asset price whose conditional variance equation follows a nonlinear asymmetric GARCH (NGARCH) process. The approximate option formula, which is just a volatility adjustment in comparison to the Black-Scholes (BS) formula, is very simple and provides the volatility term structure of spot asset prices. Also, the formula shows that the most characteristic feature of an NGARCH model appears in the vega of a European option, which depends on both the spread between the long-run variance and the current one and a parameter reproduced from the stationary property of the conditional variance. This methodology can be easily extended to an option formula for the generalized GARCH process.     

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.     

Forecasting variance using stochastic volatility and GARCH

This paper estimates the conditional variance of daily Swedish OMX-index returns with stochastic volatility (SV) models and GARCH models and evaluates the in-sample performance as well as the out-of-sample forecasting ability of the models. Asymmetric as well as weekend/holiday effects are allowed for in the variance, and the assumption that errors are Gaussian is released. Evidence is found of a leverage effect and of higher variance during weekends. In both in-sample and out-of-sample comparisons SV models outperform GARCH models. However, while asymmetry, weekend/holiday effects and non-Gaussian errors are important for the in-sample fit, it is found that these factors do not contribute to enhancing the forecasting ability of the SV models.     

Modeling Conditional Skewness in Stock Returns

Abstract

In this paper, we propose a new GARCH-in-Mean (GARCH-M) model allowing for conditional skewness. The model is based on the so-called z distribution capable of modeling skewness and kurtosis of the size typically encountered in stock return series. The need to allow for skewness can also be readily tested. The model is consistent with the volatility feedback effect in that conditional skewness is dependent on conditional variance. Compared to previously presented GARCH models allowing for conditional skewness, the model is analytically tractable, parsimonious and facilitates straightforward interpretation.Our empirical results indicate the presence of conditional skewness in the monthly postwar US stock returns. Small positive news is also found to have a smaller impact on conditional variance than no news at all. Moreover, the symmetric GARCH-M model not allowing for conditional skewness is found to systematically overpredict conditional variance and average excess returns.     

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.     

Physical delivery versus cash settlement: an empirical study on the feeder cattle contract

This paper investigates the effects of the switch from physical delivery to cash settlement on the behavior of the cash and futures prices of the feeder cattle contract traded on the Chicago Mercantile Exchange. A bivariate Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is applied to estimate the conditional volatility structure, with a possible structural break due to the switch to cash settlement. The results show that the volatility of the futures prices (but not the cash prices) declined after physical delivery was replaced by cash settlement. In terms of futures hedging, cash settlement led to smaller and more stable hedge ratios. The variance of the hedged portfolio also decreased substantially. The evidence suggests that cash settlement is beneficial to the feeder cattle futures market.     

An Assessment of Empirical Model Performance When Financial Market Transactions are Observed at Different Data Frequencies: An Application to East Asian Exchange Rates

This paper compares the performance of alternative models of east Asian exchange rates at different data frequencies. Selected models employ different specifications of the conditional variance and the conditional error distribution. Conditional variance specifications include: homoscedasticity, GARCH, LGARCH, and EGARCH. Conditional error distribution specifications include normal and Student t. The best exchange rate model specification is clearly conditional on data frequency. Higher frequency (daily, weekly) data commonly exhibit characteristics that demand more sophisticated estimation methods than analysts commonly employ. These characteristics generally vanish at lower (monthly, quarterly) frequencies. Overall we find significant benefit from accommodating heteroscedasticity and leptokurtic properties of the conditional distribution as data frequency increases. Using a likelihood ratio test we compare the relative gain from addressing heteroscedasticity (through use of GARCH models) versus accommodation of leptokurtosis. This comparison suggests that the gains from correct specification of the conditional distribution dominate those obtained from addressing problems of heteroscedasticity.     

Markov-switching in target stocks during takeover bids

This paper examines shifts in the market betas and the conditional volatility of stock prices of takeover targets. Using daily stock prices of five European and American targets, we find that adequately specified Markov-switching GARCH models are capable of detecting statistically significant regime-switches in all takeover deal-types (in cash bids, pure share-exchange bids, mixed bids). In particular, conditional volatility regime-switches are found to be most clear-cut for cash bids. Our econometric findings have implications for a broad range of financial applications such as the valuation of target stock options.     

Volatility transmission between oil prices and equity sector returns

This paper employs bivariate GARCH models to simultaneously estimate the mean and conditional variance between five different US sector indexes and oil prices. Since many different financial assets are traded based on these market sector returns, it is important for financial market participants to understand the volatility transmission mechanism over time and across these series in order to make optimal portfolio allocation decisions. We examine weekly returns from January 1, 1992 to April 30, 2008 and find evidence of significant transmission of shocks and volatility between oil prices and some of the examined market sectors. The findings support the idea of cross-market hedging and sharing of common information by investors.     

Aggregational Gaussianity and barely infinite variance in financial returns

This paper aims at reconciling two apparently contradictory empirical regularities of financial returns, namely, the fact that the empirical distribution of returns tends to normality as the frequency of observation decreases (aggregational Gaussianity) combined with the fact that the conditional variance of high frequency returns seems to have a (fractional) unit root, in which case the unconditional variance is infinite. We provide evidence that aggregational Gaussianity and infinite variance can coexist, provided that all the moments of the unconditional distribution whose order is less than two exist. The latter characterizes the case of Integrated and Fractionally Integrated GARCH processes. Finally, we discuss testing for aggregational Gaussianity under barely infinite variance. Our empirical motivation derives from commodity prices and stock indices, while our results are relevant for financial returns in general.     

GARCH option pricing models with Meixner innovations

The paper presents GARCH option pricing models with Meixner-distributed innovations. The risk-neutral dynamics are derived by means of the conditional Esscher transform. Assessing the option pricing performance both in-sample and out-of-sample, we find that the models compare favorably against the benchmark models. Simulations suggest that the driver of these results is the impact of conditional skewness and conditional excess kurtosis on option prices.     

Option pricing under regime switching

Abstract

This paper develops a family of option pricing models when the underlying stock price dynamic is modelled by a regime switching process in which prices remain in one volatility regime for a random amount of time before switching over into a new regime. Our family includes the regime switching models of Hamilton (Hamilton J 1989 Econometrica 57 357–84), in which volatility influences returns. In addition, our models allow for feedback effects from returns to volatilities. Our family also includes GARCH option models as a special limiting case. Our models are more general than GARCH models in that our variance updating schemes do not only depend on levels of volatility and asset innovations, but also allow for a second factor that is orthogonal to asset innovations. The underlying processes in our family capture the asymmetric response of volatility to good and bad news and thus permit negative (or positive) correlation between returns and volatility. We provide the theory for pricing options under such processes, present an analytical solution for the special case where returns provide no feedback to volatility levels, and develop an efficient algorithm for the computation of American option prices for the general case.     

Dynamic Volatility Trading Strategies in the Currency Option Market

The conditional volatility of foreign exchange rates can be predicted using GARCH models or implied volatility extracted from currency options. This paper investigates whether these predictions are economically meaningful in trading strategies that are designed only to trade volatility risk. First, this article provides new evidence on the issue of information content of implied volatility and GARCH volatility in forecasting future variance. In an artificial world without transaction costs both delta-neutral and straddle trading stratgies lead to significant positive profits, regardless of which volatility prediction method is used. Specifically, the agent using the Implied Stochastic Volatility Regression method (ISVR) earns larger profits than the agent using the GARCH method. Second, it suggests that the currency options market is informationally efficient. After accounting for transaction costs, which are assumed to equal one percent of option prices, observed profits are not significantly differentfrom zero in most trading strategies. Finally, these strategies offered returns have higher Sharpe ratio and lower correlation with several major asset classes. Consequently, hedge funds and institutional investors who are seeking alternative “marketneutral” investment methods can use volatility trading to improvethe risk-return profile of their portfolio through diversification. This revised version was published online in November 2006 with corrections to the Cover Date.     

Nonlinear dynamics of the Nikkei Stock Average Futures

This paper analyzes the conditional distribution of the Nikkei Stock Average Futures prices traded in the Singapore International Monetary Exchange (SIMEX). It is found that the conditional mean of the logarithmic price ratios is zero and the conditional variance is adequately described by the exponential generalized autoregressive conditional heteroscedasticity model (witht errors) suggested by Nelson (1991) and the autoregressive volatility model suggested by Hsieh (1993). The Brock, Dechert and Scheinkman (1987) statistic cannot reject the hypothesis that the standardized residuals are independently and identically distributed. The results are applied to calculate the maintenance margin and the long-term capital requirements of the contract given an assumed maximum failure rate. The margin requirements set by the SIMEX appear to be adequate compared to our estimates.     

European exchange rate volatility dynamics: an empirical investigation

The hourly and daily dummy variables in the conditional variance functions of the two European currencies, the British pound and the euro are estimated. The conditional variance functions are specified as GARCH models to capture the time-dependent conditional heteroskedasticty at both the hourly and daily recorded data. The estimated dummy variables give remarkably similar and distinct characteristics of the volatility dynamics embodied in the two currencies. Some discussion of the possible sources of the observed volatility dynamics in the two currencies is provided. A comparison between GARCH, FIGARCH and SV models is also provided. The estimated hourly and daily dummy variables suggests that euro is considerably more volatile when compared to British pound, a result with important implications for the economic policy making in the two regions.     

Domestic macroeconomic determinants of precious metals prices in developed and emerging economies: An international analysis of the long and short run

This study examines the relationship between domestic macroeconomic factors and domestic precious metals prices across developed and emerging markets from 1979 to 2020. The statistical characteristics of the domestic variables are not found to be consistent across countries, so that these relationships cannot be modelled in one specific way. To model each metal domestically, we use various time series techniques as dictated by the combined characteristics of the domestic variables.The findings of this analysis reveal relationships that are not consistent across countries or precious metals. No consistent set of variables is found to exist that can explain either the short or the long run determinants of domestic precious metals prices, and there is no clear divide between developed or emerging markets. Any model of the determinants of a precious metal's domestic price requires individual handling by the practitioners or academics undertaking it, rather than assuming a single set of determinants as is frequently done.