Forward implied volatility expansions in LSV models

In this work we address the problem of finding formulas for efficient and reliable analytical approximation for the calculation of forward implied volatility in LSV models, a problem which is reduced to the calculation of option prices as an expansion of the price of the same financial asset in a Black-Scholes dynamic. Our approach involves an expansion of the differential operator, whose solution represents the price in local stochastic volatility dynamics. Further calculations then allow to obtain an expansion of the implied volatility without the aid of any special function or expensive from the computational point of view, in order to obtain explicit formulas fast to calculate but also as accurate as possible.

The forecast performance of competing implied volatility measures:the case of individual stocks

This study examines the information content of alternative implied volatility measures for the 30 components of the Dow Jones Industrial Average Index from 1996 until 2007. Along with the popular Black-Scholes and \model-free" implied volatility expectations, the recently proposed corridor implied volatil- ity (CIV) measures are explored. For all pair-wise comparisons, it is found that a CIV measure that is closely related to the model-free implied volatility, nearly always delivers the most accurate forecasts for the majority of the firms. This finding remains consistent for different forecast horizons, volatility definitions, loss functions and forecast evaluation settings.

The meaning of implied volatility in pricing stock options traded in options markets

Ph.D. in the Faculty of Business Administration

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.

Modeling and predicting the CBOE market volatility index

This paper performs a thorough statistical examination of the time-series properties of the daily market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies not only on the widespread consensus that the VIX is a barometer of the overall market sentiment as to what concerns investors' risk appetite, but also on the fact that there are many trading strategies that rely on the VIX index for hedging and speculative purposes. Preliminary analysis suggests that the VIX index displays long-range dependence. This is well in line with the strong empirical evidence in the literature supporting long memory in both options-implied and realized variances. We thus resort to both parametric and semiparametric heterogeneous autoregressive (HAR) processes for modeling and forecasting purposes. Our main ndings are as follows. First, we con rm the evidence in the literature that there is a negative relationship between the VIX index and the S&P 500 index return as well as a positive contemporaneous link with the volume of the S&P 500 index. Second, the term spread has a slightly negative long-run impact in the VIX index, when possible multicollinearity and endogeneity are controlled for. Finally, we cannot reject the linearity of the above relationships, neither in sample nor out of sample. As for the latter, we actually show that it is pretty hard to beat the pure HAR process because of the very persistent nature of the VIX index.

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.

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.

Examining and Modeling the Dynamics of the Volatility Surface

The objective of this paper is to investigate and model the characteristics of the prevailing volatility smiles and surfaces on the DAX- and ESX-index options markets. Continuing on the trend of Implied Volatility Functions, the Standardized Log-Moneyness model is introduced and fitted to historical data. The model replaces the constant volatility parameter of the Black & Scholes pricing model with a matrix of volatilities with respect to moneyness and maturity and is tested out-of-sample. Considering the dynamics, the results show support for the hypotheses put forward in this study, implying that the smile increases in magnitude when maturity and ATM volatility decreases and that there is a negative/positive correlation between a change in the underlying asset/time to maturity and implied ATM volatility. Further, the Standardized Log-Moneyness model indicates an improvement to pricing accuracy compared to previous Implied Volatility Function models, however indicating that the parameters of the models are to be re-estimated continuously for the models to fully capture the changing dynamics of the volatility smiles.

Smiling under stochastic volatility

This paper studies the behavior of the implied volatility function (smile) when the true distribution of the underlying asset is consistent with the stochastic volatility model proposed by Heston (1993). The main result of the paper is to extend previous results applicable to the smile as a whole to alternative degrees of moneyness. The conditions under which the implied volatility function changes whenever there is a change in the parameters associated with Hestons stochastic volatility model for a given degree of moneyness are given.

Nonparametric estimation of the leverage effect: a trade-off between robustness and efficiency

We consider two new approaches to nonparametric estimation of the leverage effect. The first approach uses stock prices alone. The second approach uses the data on stock prices as well as a certain volatility instrument, such as the CBOE volatility index (VIX) or the Black-Scholes implied volatility. The theoretical justification for the instrument-based estimator relies on a certain invariance property, which can be exploited when high frequency data is available. The price-only estimator is more robust since it is valid under weaker assumptions. However, in the presence of a valid volatility instrument, the price-only estimator is inefficient as the instrument-based estimator has a faster rate of convergence. We consider two empirical applications, in which we study the relationship between the leverage effect and the debt-to-equity ratio, credit risk, and illiquidity.

The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.

Contemporaneous intra-day volume, option, and futures volatility transmissions across parallel markets

The primary objective of this article is to investigate volatility transmission across three parallel markets operating on the Sydney Futures Exchange (SFE), both within and out of sample. Half-hourly observations are sampled from transaction data for the share price index (SPI) futures, SPI futures options, and 90-day bank accepted bill (BAB) futures markets, and the analysis is carried out using the simultaneous volatility (SVL) system of equations as well as competing volatility models. The results confirm the poor ability of GARCH models to fit intraday data. This study also applies an artificial nesting procedure to evaluate the out-of-sample volatility forecasts. Implied volatility has very limited (if any) predictive power when evaluated in isolation, whereas the SVL model with implied volatility embedded provides incremental information relative to competing model forecasts.

Do retail option traders know better about market volatility?

This paper examines the informational content and predictive power of implied volatility over different forecasting horizons in a sample of European covered warrants traded in the Hong Kong and Singapore markets. The empirical results show that time-series-based volatility forecasts outperform implied volatility forecast as a predictor of future volatility. The finding also suggests that implied volatility is biased and informationally inefficient. The results are attributable to the fact in Hong Kong and Singapore the covered warrants markets are dominated by retail investors, who tend to use covered warrants' leverage to speculate on the price movements of the underlying rather than to express their view on volatility.