Time-varying Conditional Volatility Research Articles

On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity

In this paper, we consider a novel approach for the fair valuation of a participating life insurance policy when the dynamics of the reference portfolio underlying the policy are governed by an Asymmetric Power GARCH (APGARCH) model with innovations having a general parametric distribution. The APGARCH model provides a flexible way to incorporate the effect of conditional heteroscedasticity or time-varying conditional volatility and nests a number of important symmetric or asymmetric ARCH-type models in the literature. It also provides a flexible way to capture both the memory effect of the conditional volatility and the asymmetric effects of past positive and negative returns on the current conditional volatility, called the leverage effect. The key valuation tool here is the conditional Esscher transform of Buhlmann et al. (1996, 1998). The conditional Esscher transform provides a convenient and flexible way for the fair valuation under different specifications of the conditional heteroscedastic models. We illustrate the practical implementation of the model using the S&P 500 index as a proxy for the reference portfolio. We also conduct sensitivity analysis of the fair value of the policy with respect to the parameters in the APGARCH model to document the impacts of different conditional volatility models nested in the APGARCH model and the leverage effect on the fair value. The results of the analysis reveal that the memory effect of the conditional volatility has more significant impact on the fair value of the policy than the leverage effect.

The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR

This paper investigates the role of high-order moments in the estimation of conditional value at risk (VaR). We use the skewed generalized t distribution (SGT) with time-varying parameters to provide an accurate characterization of the tails of the standardized return distribution. We allow the high-order moments of the SGT density to depend on the past information set, and hence relax the conventional assumption in conditional VaR calculation that the distribution of standardized returns is iid. The maximum likelihood estimates show that the time-varying conditional volatility, skewness, tail-thickness, and peakedness parameters of the SGT density are statistically significant. The in-sample and out-of-sample performance results indicate that the conditional SGT-GARCH approach with autoregressive conditional skewness and kurtosis provides very accurate and robust estimates of the actual VaR thresholds.

Role of Autoregressive Conditional Skewness and Kurtosis in the Estimation of Conditional VaR

This paper investigates the role of high-order moments in the estimation of conditional value at risk (VaR). We use the skewed generalized t distribution (SGT) with time-varying parameters to provide an accurate characterization of the tails of the standardized return distribution. We allow the high-order moments of the SGT density to depend on the past information set, and hence relax the conventional assumption in conditional VaR calculation that the distribution of standardized returns is iid. The maximum likelihood estimates show that the time-varying conditional volatility, skewness, tail-thickness, and peakedness parameters of the SGT density are statistically significant. The in-sample and out-of-sample performance results indicate that the conditional SGT-GARCH approach with autoregressive conditional skewness and kurtosis provides very accurate and robust estimates of the actual VaR thresholds.

Speculation and destabilisation

In the context of flexible exchange rates, Milton Friedman proposed that speculation must exert a stabilising influence on prices to remain profitable. This generated a substantial amount of predominantly theoretical research into the behaviour of speculators, for which the results seem to depend critically upon the assumptions. Such theoretical models need to be tested against empirical evidence to determine whether speculators behave in a destabilising manner. Using recent theoretical developments in the literature on modelling financial volatility, this paper tests the significance of speculators and their contributions to describing weekly volatilities across a series of currency, metals and commodity markets. As the time-varying conditional volatility GARCH model and its variants have been criticised for lacking economic content, incorporating speculators into such models contributes to an accommodation of this criticism. The economic implications from establishing the importance of speculators are far-reaching. Policymakers often discuss the imposition of a Tobin tax to curb speculation, so it must be established that speculators behave in economically destructive ways. The inclusion of speculators is also likely to yield superior forecasting models of volatility, and hence more efficient pricing of derivative instruments.

PRICING AUSTRALIAN S&P200 OPTIONS: A BAYESIAN APPROACH BASED ON GENERALIZED DISTRIBUTIONAL FORMS

SummaryThis paper develops a new class of option price models and applies it to options on the Australian S&P200 Index. The class of models generalizes the traditional Black‐Scholes framework by accommodating time‐varying conditional volatility, skewness and excess kurtosis in the underlying returns process. An important property of these more general pricing models is that the computational requirements are essentially the same as those associated with the Black‐Scholes model, with both methods being based on one‐dimensional integrals. Bayesian inferential methods are used to evaluate a range of models nested in the general framework, using observed market option prices. The evaluation is based on posterior parameter distributions, as well as posterior model probabilities. Various fit and predictive measures, plus implied volatility graphs, are also used to rank the alternative models. The empirical results provide evidence that time‐varying volatility, leptokurtosis and a small degree of negative skewness are priced in Australian stock market options.

Monetary policy shocks:☆Testing identification conditions under time-varying conditional volatility

Abstract We propose an empirical procedure, which exploits the conditional heteroscedasticity of fundamental disturbances, to test the targeting and orthogonality restrictions imposed in the recent VAR literature to identify monetary policy shocks. Based on U.S. monthly data for the post-1982 period, we reject the non-borrowed-reserve and interest-rate targeting procedures. In contrast, we present evidence supporting targeting procedures implying more than one policy variable. We also always reject the orthogonality conditions between policy shocks and macroeconomic variables. We show that using invalid restrictions often produces misleading policy measures and dynamic responses. These results have important implications for the measurement of policy shocks and their temporal effects as well as for the estimation of the monetary authority's reaction function.

Monetary policy shocks:: Testing identification conditions under time-varying conditional volatility

We propose an empirical procedure, which exploits the conditional heteroscedasticity of fundamental disturbances, to test the targeting and orthogonality restrictions imposed in the recent VAR literature to identify monetary policy shocks. Based on U.S. monthly data for the post-1982 period, we reject the non-borrowed-reserve and interest-rate targeting procedures. In contrast, we present evidence supporting targeting procedures implying more than one policy variable. We also always reject the orthogonality conditions between policy shocks and macroeconomic variables. We show that using invalid restrictions often produces misleading policy measures and dynamic responses. These results have important implications for the measurement of policy shocks and their temporal effects as well as for the estimation of the monetary authority's reaction function.

GARCH, jumps and permanent and transitory components of volatility: the case of the Taiwan exchange rate

This paper investigates whether there are three distinctive features in financial asset prices, that is, time-varying conditional volatility, jumps and the component factors of volatility. It adopts a component-GARCH-Jump, which can efficiently capture the three features simultaneously. Our results demonstrate that the three features exist in the Taiwan exchange rate. Besides time-varying conditional volatility, our model identifies 172 jumps between 5 January 1988 and 21 March 2003. The empirical evidence shows that the permanent component of the conditional variance is a relatively smooth movement except for a fairly sharp shift which began in 1997. This means that the effect of the Asian crisis shock might very well have exerted not only a transitory jump effect, but also a permanent effect on Taiwan’s exchange rate.

Can the Random Walk Model be Beaten in Out-of-Sample Density Forecasts: Evidence from Intraday Foreign Exchange Rates

Numerous studies have shown that the simple random walk model outperforms all structural and time series models in forecasting the conditional mean of exchange rate changes. However, in many important applications, such as risk management, forecasts of the probability distribution of exchange rate changes are often needed. In this paper, we develop a nonparametric portmanteau evaluation procedure for out-of-sample density forecast and provide a comprehensive empirical study on the out-of-sample performance of a wide variety of time series models in forecasting the intraday probability density of two major exchange rates - Euro/Dollar and Yen/Dollar. We find that some nonlinear time series models provide better density forecast than the simple random walk model, although they underperform in forecasting the conditional mean. For Euro/Dollar, it is important to model heavy tails through a Student-t innovation and asymmetric timevarying conditional volatility through a regime-switching GARCH model for both insample and out-of-sample performance; modeling conditional mean and serial dependence in higher order moments (e.g., conditional skewness), although important for in-sample performance, does not help out-of-sample density forecast. For Yen/Dollar, it is also important to model heavy tails and volatility clustering, and the best density forecast model is a RiskMetrics model with a Student-t innovation. As a simple application, we find that the models that provide good density forecast generally provide good forecast of Value-at-Risk.

Non-linear dependence in inter-war exchange rates: some further evidence

This paper reconsiders the time-series properties of inter-war pound-franc and pound-dollar exchange rate returns in the context of a smooth transition variant of the threshold autoregressive model. It is found that autoregressive structure in returns is largely confined to values in proximity with thresholds which are possibly associated with market intervention points or market sentiment. Under joint estimation in conjunction with GARCH models of time-varying conditional volatility, these models satisfactorily capture all non-linearity in the data, and in the case of pound-dollar returns provide out-of-sample forecasts superior to alternative linear and non-linear models previously considered in the literature.

Time-varying risk premia, volatility, and technical trading rule profits: Evidence from foreign currency futures markets

This paper re-examines the efficiency of foreign currency futures markets by evaluating the role of time-varying risk premia and volatility in explaining technical trading rule profits. The results show that large parts of the technical rule profits can be explained by the time-varying risk premia estimated from a general model for the conditional CAPM; The bootstrap distributions for the profits under the null model average one-third to one-half of the actual profits and enclose the actual profits well within the 90% confidence intervals. Time-varying conditional volatility explains an additional 10% of the profits.

Policy and volatility of asset returns

During the last 10 years, a number of papers documented the time-varying conditional volatility of asset returns. Although these papers contribute significantly to our understanding of the nature of volatility, they do not typically provide an economic explanation of volatility. One possibly important variable that is correlated with volatility is policy. This paper examines the connection between volatility and policy in the context of two very closely watched actions of the Federal Reserve: open market operations in the domestic market, and sterilized intervention in the foreign exchange market. The results of the paper suggest that policy responds to volatility in the exchange rates and also to volatility in short-term interest rates. Additionally, there is some evidence indicating that policy reduces volatility in asset returns.