The relationship between implied and realized volatility : evidence from the Australian stock index option market

This paper examines the relationship between the volatility implied in option prices and the subsequently realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) during a period of 5 years. Unlike stock index options such as the S&P 100 index options in the US market, the S&P/ASX 200 index options are traded infrequently and in low volumes, and have a long maturity cycle. Thus an errors-in-variables problem for measurement of implied volatility is more likely to exist. After accounting for this problem by instrumental variable method, it is found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future volatility.

Forecasting volatility and correlation : the role of option implied measures

Forecasts of volatility and correlation are important inputs into many practical financial problems. Broadly speaking, there are two ways of generating forecasts of these variables. Firstly, time-series models apply a statistical weighting scheme to historical measurements of the variable of interest. The alternative methodology extracts forecasts from the market traded value of option contracts. An efficient options market should be able to produce superior forecasts as it utilises a larger information set of not only historical information but also the market equilibrium expectation of options market participants. While much research has been conducted into the relative merits of these approaches, this thesis extends the literature along several lines through three empirical studies. Firstly, it is demonstrated that there exist statistically significant benefits to taking the volatility risk premium into account for the implied volatility for the purposes of univariate volatility forecasting. Secondly, high-frequency option implied measures are shown to lead to superior forecasts of the intraday stochastic component of intraday volatility and that these then lead on to superior forecasts of intraday total volatility. Finally, the use of realised and option implied measures of equicorrelation are shown to dominate measures based on daily returns.

Essays on volatility and liquidity in financial markets

The price formation of financial assets is a complex process. It extends beyond the standard economic paradigm of supply and demand to the understanding of the dynamic behavior of price variability, the price impact of information, and the implications of trading behavior of market participants on prices. In this thesis, I study aggregate market and individual assets volatility, liquidity dimensions, and causes of mispricing for US equities over a recent sample period. How volatility forecasts are modeled, what determines intradaily jumps and causes changes in intradaily volatility and what drives the premium of traded equity indexes? Are they induced, for example, by the information content of lagged volatility and return parameters or by macroeconomic news, changes in liquidity and volatility? Besides satisfying our intellectual curiosity, answers to these questions are of direct importance to investors developing trading strategies, policy makers evaluating macroeconomic policies and to arbitrageurs exploiting mispricing in exchange-traded funds. Results show that the leverage effect and lagged absolute returns improve forecasts of continuous components of daily realized volatility as well as jumps. Implied volatility does not subsume the information content of lagged returns in forecasting realized volatility and its components. The reported results are linked to the heterogeneous market hypothesis and demonstrate the validity of extending the hypothesis to returns. Depth shocks, signed order flow, the number of trades, and resiliency are the most important determinants of intradaily volatility. In contrast, spread shock and resiliency are predictive of signed intradaily jumps. There are fewer macroeconomic news announcement surprises that cause extreme price movements or jumps than those that elevate intradaily volatility. Finally, the premium of exchange-traded funds is significantly associated with momentum in net asset value and a number of liquidity parameters including the spread, traded volume, and illiquidity. The mispricing of industry exchange traded funds suggest that limits to arbitrage are driven by potential illiquidity.

Are combination forecasts of S&P 500 volatility statistically superior?

Forecasting volatility has received a great deal of research attention, with the relative performances of econometric model based and option implied volatility forecasts often being considered. While many studies find that implied volatility is the pre-ferred approach, a number of issues remain unresolved, including the relative merit of combining forecasts and whether the relative performances of various forecasts are statistically different. By utilising recent econometric advances, this paper considers whether combination forecasts of S&P 500 volatility are statistically superior to a wide range of model based forecasts and implied volatility. It is found that a combination of model based forecasts is the dominant approach, indicating that the implied volatility cannot simply be viewed as a combination of various model based forecasts. Therefore, while often viewed as a superior volatility forecast, the implied volatility is in fact an inferior forecast of S&P 500 volatility relative to model-based forecasts.

Yield-factor volatility models

The term structure of interest rates is often summarized using a handful of yield factors that capture shifts in the shape of the yield curve. In this paper, we develop a comprehensive model for volatility dynamics in the level, slope, and curvature of the yield curve that simultaneously includes level and GARCH effects along with regime shifts. We show that the level of the short rate is useful in modeling the volatility of the three yield factors and that there are significant GARCH effects present even after including a level effect. Further, we find that allowing for regime shifts in the factor volatilities dramatically improves the model’s fit and strengthens the level effect. We also show that a regime-switching model with level and GARCH effects provides the best out-of-sample forecasting performance of yield volatility. We argue that the auxiliary models often used to estimate term structure models with simulation-based estimation techniques should be consistent with the main features of the yield curve that are identified by our model.

The jump component of S&P 500 volatility and the VIX index

Much research has investigated the differences between option implied volatilities and econometric model-based forecasts. Implied volatility is a market determined forecast, in contrast to model-based forecasts that employ some degree of smoothing of past volatility to generate forecasts. Implied volatility has the potential to reflect information that a model-based forecast could not. This paper considers two issues relating to the informational content of the S&P 500 VIX implied volatility index. First, whether it subsumes information on how historical jump activity contributed to the price volatility, followed by whether the VIX reflects any incremental information pertaining to future jump activity relative to model-based forecasts. It is found that the VIX index both subsumes information relating to past jump contributions to total volatility and reflects incremental information pertaining to future jump activity. This issue has not been examined previously and expands our understanding of how option markets form their volatility forecasts.

The benefit of modeling jumps in realized volatility for risk prediction : evidence from Chinese mainland stocks

Recent literature has focused on realized volatility models to predict financial risk. This paper studies the benefit of explicitly modeling jumps in this class of models for value at risk (VaR) prediction. Several popular realized volatility models are compared in terms of their VaR forecasting performances through a Monte Carlo study and an analysis based on empirical data of eight Chinese stocks. The results suggest that careful modeling of jumps in realized volatility models can largely improve VaR prediction, especially for emerging markets where jumps play a stronger role than those in developed markets.

Modeling multivariate autoregressive conditional heteroskedasticity with the double smooth transition conditional correlation GARCH Model

In this paper, we propose a multivariate GARCH model with a time-varying conditional correlation structure. The new double smooth transition conditional correlation (DSTCC) GARCH model extends the smooth transition conditional correlation (STCC) GARCH model of Silvennoinen and Teräsvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC-GARCH model, and another one to test for another transition in the STCC-GARCH framework. In addition, other specification tests, with the aim of aiding the model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. Applying the model to the stock and bond futures data, we discover that the correlation pattern between them has dramatically changed around the turn of the century. The model is also applied to a selection of world stock indices, and we find evidence for an increasing degree of integration in the capital markets.

Modeling conditional correlations of asset returns : a smooth transition approach

In this paper we propose a new multivariate GARCH model with time-varying conditional correlation structure. The time-varying conditional correlations change smoothly between two extreme states of constant correlations according to a predetermined or exogenous transition variable. An LM–test is derived to test the constancy of correlations and LM- and Wald tests to test the hypothesis of partially constant correlations. Analytical expressions for the test statistics and the required derivatives are provided to make computations feasible. An empirical example based on daily return series of five frequently traded stocks in the S&P 500 stock index completes the paper.