Ser-Huang Poon

Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns

The information content of implied volatilities and intraday returns is compared in the context of forecasting index volatility over horizons from 1 to 20 days. Forecasts of two measures of realized volatility are obtained after estimating ARCH models using daily index returns, daily observations of the VIX index of implied volatility, and sums of squares of 5-min index returns. The in-sample estimates show that nearly all relevant information is provided by the VIX index, and hence there is not much incremental information in high-frequency index returns. For out-of-sample forecasting, the VIX index provides the most accurate forecasts for all forecast horizons and performance measures considered. The evidence for incremental forecasting information in intraday returns is insignificant.

Returns Synchronization and Daily Correlation Dynamics Between International Stock Markets

The use of close-to-close returns underestimates returns correlation because international stock markets have different trading hours. With the availability of 16:00 (London time) stock market series, we find dynamics of daily correlation and covariance, estimated using two non-synchroneity adjustment procedures, to be substantially different from their synchronous counterparts. Conditional correlation may have different signs depending on the model and data type used. Other findings include volatility spillover from the US to the UK (and France), and a reverse spillover which is not documented before. Also, unlike previous findings, we found the increase in daily correlation is prominent only under extremely adverse conditions when a large negative return has been registered.

Practical Issues in Forecasting Volatility

A comparison is presented of 93 studies that conducted tests of volatility-forecasting methods on a wide range of financial asset returns. The survey found that option-implied volatility provides more accurate forecasts than time-series models. Among the time-series models, no model is a clear winner, although a possible ranking is as follows: historical volatility, generalized autoregressive conditional heteroscedasticity, and stochastic volatility. The survey produced some practical suggestions for volatility forecasting. Volatility forecasting plays an important role in investment, option pricing, and risk management. In this article, we summarize our review of 93 papers devoted to comparing the forecasting power of various volatility models reported in the past 20 years. The definition of volatility is taken to be standard deviation of returns. The assets studied in these 93 papers included stock indexes, stocks, exchange rates, and interest rates from both developed and emerging financial markets. The forecast horizon ranged from one hour to one year (with a few exceptions that extended the forecast horizon to 30 months and to five years). The review covers three main categories of time-series model—historical volatility, autoregressive conditional heteroscedasticity (ARCH), and stochastic volatility (SV)—and the method of deriving implied volatility from option prices. We introduce the four models, discuss some characteristics of financial market volatility, and describe the common objectives of volatility forecasting that have a direct impact on choice of volatility model and the criteria for evaluating forecasts. Using recent research, we provide some insights into the effect of outliers, make some suggestions as to how they might be handled, and provide some practical advice for volatility forecasters. We also offer a broad-based ranking of the four volatility-forecasting models. Financial market volatility is clearly forecastable. Research has shown that the forecasting power for stock index volatility is 50–58 percent for horizons of 1 to 20 trading days. The one-day-ahead forecasting record for exchange rates is 10–15 percent, and it is likely to increase by about threefold if ex post volatility is measured more accurately. The one-week-ahead and one-month-ahead records for short-term interest rates have been documented as, respectively, 8 percent and 24 percent. Based on the forecasting results reported in the studied papers, option-implied volatility dominates time-series models because the market option price fully incorporates current information and future volatility expectations. Between historical volatility and ARCH models, we found no clear winner, but they are both better than the stochastic volatility model. Despite the added flexibility and complexity of the SV model, we found no clear evidence that it provides superior volatility forecasts. Also, high-frequency data clearly provide more information and produce better volatility forecasts, particularly over short horizons. The conclusion that option-implied volatility forecasting provides the best forecast does not violate market efficiency because accurate volatility forecasting is not in conflict with underlying asset and option prices being correct. Options are not available for all assets, so using historical volatility must be considered. These models are not necessarily less sophisticated than ARCH models. For example, the realized-volatility model is classified as a historical volatility model. The important aspects of using historical models are (1) that actual volatility must be measured accurately and (2) that when high-frequency data are available, such information improves volatility estimation and forecasts.

Modelling Extreme-Value Dependence in International Stock Markets

In the finance literature, cross-sectional dependence in extreme returns of risky assets is often modelled implicitly assuming an asymptotically dependent structure. If the true dependence structure is asymptotically independent then current modelling approaches will lead to an over-estimation of the risk of simultaneous extreme events. We use two simple nonparametric measures to identify and quantify the tail dependence among stock returns in five international stock markets. We show that there is strong evidence in favour of asymptotically independent models for the tail structure of stock market returns, and that most of the extremal dependence is due to heteroskedasticity in stock returns processes. Using a range of volatility filters, we find that tail index and tail dependence can be partially captured by models for heteroskedasticity. But, from our findings, there is no clear distinction that would lead us to prefer one volatility filter over another.

Hedging the Black Swan: Conditional Heteroskedasticity and Tail Dependence in S&P500 and Vix

The recent financial crisis has accentuated the fact that extreme outcomes have been overlooked and not dealt with adequately. While extreme value theories have existed for a long time, the multivariate variant is difficult to handle in the financial markets due to the prevalent heteroskedasticity embedded in most financial time series, and the complex extremal dependence that cannot be conveniently captured by a single structure. Moreover, most of the existing approaches are based on a limiting argument in which all variables become large at the same rate. In this paper, we show how the conditional approach of Heffernan and Tawn (2004) can be implemented to model extremal dependence between financial time series. We use a hedging example based on VIX futures to demonstrate the flexibility and superiority of the conditional approach against the conventional OLS regression approach.

Modelling S&P 100 Volatility: The Information Content of Stock Returns

Hitherto, index volatility has been modelled using the history of index returns but not the returns histories of the stocks that define the index. Theoretical models that relate volatility to the quantity of information are extended to a multi-asset setting and it is deduced that stock returns may or may not have incremental information when modelling index volatility, depending on the sources of information that move stock prices. The first empirical study that can help resolve this theoretical uncertainty is presented. A detailed analysis of a daily volatility of the S&P 100 index from 1983 to 1992 shows there is some incremental volatility information in the returns from the 100 shares that define the index. ARCH models are estimated, that incorporate leverage effects, dummy variables for the 1987 crash and aggregate measures of stock return volatility. Parameter estimates for several stock measures reject the null hypothesis that these measures are irrelevant, at the 5% level, for the ten years considered. Mixed results are obtained for sub-periods. Significant differences between estimated volatilities are found, leaving open the possibility that the new volatility estimates may price options differently, by amounts that are of economic significance.

A Source of Long Memory in Volatility

The long memory characteristic of financial market volatility is well documented and has important implications for volatility forecasting and option pricing. When fitted to the same data, different volatility models calculate the unconditional variance differently and could have very different volatility persistent parameters. Hence, they produce very different volatility forecasts even when the projection is just beyond a few days. The popular GARCH and GJR models have short memory. This paper compares the out-of-sample forecasting performance of four long memory volatility models, viz. fractional integrated (FI), break, component and regime switching. Using S&P 500 returns, we find structural break model to produce the best in-sample fit and out-of-sample forecasts, if future volatility breaks are known. Without knowing the future breaks, GJR produced the best short horizon forecasts. For volatility forecasts of 10 days and beyond, FI dominates. The FI model projects the future unconditional variance from the exponentially weighted sum of an infinite number of past shocks. The persistence parameters then control how fast the forecasts converge to this unconditional variance. As the fractional differencing parameter gets closer to and exceeds 0.5, volatility is non-stationary. The success of the FI model in forecasting S&P 500 volatility suggests that the latter should be treated as nonstationary. Which volatility model is best for forecasting is an empirical issue. A best model for S&P 500 need not be the best for the other series, and may not always be the best, all the time, for forecasting S&P 500 volatility. Unusual events such as the 1987 crash, for example, call for unusual treatments to get better forecasting performance.

GDP Linked Bonds: Contract Design and Pricing

GDP linked bonds have their cashflows linked to a countrys national output. We present a model of sovereign default that tracks the sovereigns capacity to pay through the real exchange rate and potential output. By calibrating to a vanilla bond, our model produces default profiles and prices for GDP linked bonds. We evaluate the models empirical performance by pricing Argentinas GDP warrants. We then examine the effect on the cost of borrowing and default probability of several indexation schemes and show how our model can identify indexation schemes best suited to countries in different economic circumstances.

Belief rule-based system for portfolio optimisation with nonlinear cash-flows and constraints

A belief rule-based (BRB) system is a generic nonlinear modelling and inference scheme. It is based on the concept of belief structures and evidential reasoning (ER), and has been shown to be capable of capturing complicated nonlinear causal relationships between antecedent attributes and consequents. The aim of this paper is to develop a BRB system that complements the RiskMetrics WealthBench system for portfolio optimisation with nonlinear cash-flows and constraints. Two optimisation methods are presented to locate efficient portfolios under different constraints specified by the investors. Numerical studies demonstrate the effectiveness and efficiency of the proposed methodology.

Chapter 9 A Source of Long Memory in Volatility

This paper compares the out-of-sample forecasting performance of three long-memory volatility models (i.e., fractionally integrated (FI), break and regime switching) against three short-memory models (i.e., GARCH, GJR and volatility component). Using S&P 500 returns, we find that structural break models produced the best out-of-sample forecasts, if future volatility breaks are known. Without knowing the future breaks, GJR models produced the best short-horizon forecasts and FI models dominated for volatility forecasts of 10 days and beyond. The results suggest that S&P 500 volatility is non-stationary at least in some time periods. Controlling for extreme events (e.g., the 1987 crash) significantly improved forecasting performance.