Learning to act in uncertain environments : technical perspective

The problem of decision making in an uncertain environment arises in many diverse contexts: deciding whether to keep a hard drive spinning in a net-book; choosing which advertisement to post to a Web site visitor; choosing how many newspapers to order so as to maximize profits; or choosing a route to recommend to a driver given limited and possibly out-of-date information about traffic conditions. All are sequential decision problems, since earlier decisions affect subsequent performance; all require adaptive approaches, since they involve significant uncertainty. The key issue in effectively solving problems like these is known as the exploration/exploitation trade-off: If I am at a cross-roads, when should I go in the most advantageous direction among those that I have already explored, and when should I strike out in a new direction, in the hopes I will discover something better?

Comparing different explanations of the volatility trend

We analyze the puzzling behavior of the volatility of individual stock returns over the past few decades. The literature has provided many different explanations to the trend in volatility and this paper tests the viability of the different explanations. Virtually all current theoretical arguments that are provided for the trend in the average level of volatility over time lend themselves to explanations about the difference in volatility levels between firms in the cross-section. We therefore focus separately on the cross-sectional and time-series explanatory power of the different proxies. We fail to find a proxy that is able to explain both dimensions well. In particular, we find that Cao et al. [Cao, C., Simin, T.T., Zhao, J., 2008. Can growth options explain the trend in idiosyncratic risk? Review of Financial Studies 21, 2599–2633] market-to-book ratio tracks average volatility levels well, but has no cross-sectional explanatory power. On the other hand, the low-price proxy suggested by Brandt et al. [Brandt, M.W., Brav, A., Graham, J.R., Kumar, A., 2010. The idiosyncratic volatility puzzle: time trend or speculative episodes. Review of Financial Studies 23, 863–899] has much cross-sectional explanatory power, but has virtually no time-series explanatory power. We also find that the different proxies do not explain the trend in volatility in the period prior to 1995 (R-squared of virtually zero), but explain rather well the trend in volatility at the turn of the Millennium (1995–2005).

Evaluating multivariate volatility forecasts : how effective are statistical and economic loss functions?

Multivariate volatility forecasts are an important input in many financial applications, in particular portfolio optimisation problems. Given the number of models available and the range of loss functions to discriminate between them, it is obvious that selecting the optimal forecasting model is challenging. The aim of this thesis is to thoroughly investigate how effective many commonly used statistical (MSE and QLIKE) and economic (portfolio variance and portfolio utility) loss functions are at discriminating between competing multivariate volatility forecasts. An analytical investigation of the loss functions is performed to determine whether they identify the correct forecast as the best forecast. This is followed by an extensive simulation study examines the ability of the loss functions to consistently rank forecasts, and their statistical power within tests of predictive ability. For the tests of predictive ability, the model confidence set (MCS) approach of Hansen, Lunde and Nason (2003, 2011) is employed. As well, an empirical study investigates whether simulation findings hold in a realistic setting. In light of these earlier studies, a major empirical study seeks to identify the set of superior multivariate volatility forecasting models from 43 models that use either daily squared returns or realised volatility to generate forecasts. This study also assesses how the choice of volatility proxy affects the ability of the statistical loss functions to discriminate between forecasts. Analysis of the loss functions shows that QLIKE, MSE and portfolio variance can discriminate between multivariate volatility forecasts, while portfolio utility cannot. An examination of the effective loss functions shows that they all can identify the correct forecast at a point in time, however, their ability to discriminate between competing forecasts does vary. That is, QLIKE is identified as the most effective loss function, followed by portfolio variance which is then followed by MSE. The major empirical analysis reports that the optimal set of multivariate volatility forecasting models includes forecasts generated from daily squared returns and realised volatility. Furthermore, it finds that the volatility proxy affects the statistical loss functions’ ability to discriminate between forecasts in tests of predictive ability. These findings deepen our understanding of how to choose between competing multivariate volatility forecasts.

An infinite-horizon robust filter for uncertain hidden Markov Models with conditional relative entropy constraints

We consider a robust filtering problem for uncertain discrete-time, homogeneous, first-order, finite-state hidden Markov models (HMMs). The class of uncertain HMMs considered is described by a conditional relative entropy constraint on measures perturbed from a nominal regular conditional probability distribution given the previous posterior state distribution and the latest measurement. Under this class of perturbations, a robust infinite horizon filtering problem is first formulated as a constrained optimization problem before being transformed via variational results into an unconstrained optimization problem; the latter can be elegantly solved using a risk-sensitive information-state based filtering.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.

Semi-parametric forecasting of realized volatility

Forecasts generated by time series models traditionally place greater weight on more recent observations. This paper develops an alternative semi-parametric method for forecasting that does not rely on this convention and applies it to the problem of forecasting asset return volatility. In this approach, a forecast is a weighted average of historical volatility, with the greatest weight given to periods that exhibit similar market conditions to the time at which the forecast is being formed. Weighting is determined by comparing short-term trends in volatility across time (as a measure of market conditions) by means of a multivariate kernel scheme. It is found that the semi-parametric method produces forecasts that are significantly more accurate than a number of competing approaches at both short and long forecast horizons.

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.

On the efficacy of techniques for evaluating multivariate volatility forecasts

The performance of techniques for evaluating multivariate volatility forecasts are not yet as well understood as their univariate counterparts. This paper aims to evaluate the efficacy of a range of traditional statistical-based methods for multivariate forecast evaluation together with methods based on underlying considerations of economic theory. It is found that a statistical-based method based on likelihood theory and an economic loss function based on portfolio variance are the most effective means of identifying optimal forecasts of conditional covariance matrices.

Volunteers 'piggy-backing' on their private insurance : an uncertain protection against liability

Volunteering is a very important part of life in Australia with an estimated 36% of the adult population volunteering in 2010. Voluntary work generates economic benefits, addresses community needs and develops the social networks that form the backbone of civil society. Without volunteers, many essential services would either cease to exist or become too expensive for many people to afford. These volunteers, who by definition are not in receipt of any remuneration for their work and services, are exposed to personal injury and to legal liability in the discharge of their functions. It is therefore appropriate that statutory protection is extended to volunteers and that volunteer organisations procure public liability and personal accident cover where possible. However, given the patchwork quilt of circumstances where statutory or institutional cover is available to volunteers and the existence of many and diverse exclusions, it is important to have regard also to what scope a volunteer may have to avail themselves of protection against liability for volunteering activity by relying upon their own personal insurance cover. This article considers the extent of private insurance cover and its availability to volunteers under home and contents insurance and under comprehensive motor vehicle insurance. The most common policies in the Australian market are examined and the uncertain nature of protection against liability afforded by these policies is discussed. This uncertainty could be reduced should the Federal Government through amendments to the Insurance Contracts Regulations standardise the circumstances and extent to which liability protection was afforded to an insured holding home and contents insurance and comprehensive motor vehicle insurance cover.

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.

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.

Effect of atmospheric ageing on volatility and ROS of biodiesel exhaust nano-particles

Generally, the magnitude of pollutant emissions from diesel engines is ultimately coupled to the structure of fuel molecules. The presence of oxygen, level of unsaturation and the carbon chain length of respective molecules influence the combustion chemistry. It is speculated that increased oxygen content in the fuel may lead to the increased oxidative potential (Stevanovic, S. 2013). Also, upon the exposure to UV and ozone in the atmosphere, the chemical composition of the exhaust is changed. The presence of an oxidant and UV is triggering the cascade of photochemical reactions as well as the partitioning of semi-volatile compounds between the gas and particle phase. To gain an insight into the relationship between the molecular structures of the esters, their volatile organic content and the potential toxicity of diesel exhaust particulate matter, measurements were conducted on a modern common rail diesel engine. This research also investigates the contribution of atmospheric conditions on the transfer of semi-volatile fraction of diesel exhaust from the gas phase to the particle phase and the extent to which semi-volatile compounds (SVOCs) are related to the oxidative potential, expressed through the concentration of reactive oxygen species (ROS) (Stevanovic, S. 2013)...

Volatility timing : how best to forecast portfolio exposures

This paper investigates how best to forecast optimal portfolio weights in the context of a volatility timing strategy. It measures the economic value of a number of methods for forming optimal portfolios on the basis of realized volatility. These include the traditional econometric approach of forming portfolios from forecasts of the covariance matrix, and a novel method, where a time series of optimal portfolio weights are constructed from observed realized volatility and directly forecast. The approach proposed here of directly forecasting portfolio weights shows a great deal of merit. Resulting portfolios are of equivalent economic benefit to a number of competing approaches and are more stable across time. These findings have obvious implications for the manner in which volatility timing is undertaken in a portfolio allocation context.