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.

15 year old volens to BMX riding risks

The Queensland Court of Appeal recently heard a case that raised the defence of volenti on fit injuria. By a majority of 2:1 the court held in Leyden v Caboolture Shire Council [2007] QCA 134 (20 April 2007) that the defence of volenti was established and defeated the action in negligence for damages for personal injury. The facts of the case were quite simple. The plaintiff was 15 years old when he was injured at the Bluebell Park which was controlled and managed by the Caboolture Shire Council (the defendant). The park had a BMX track – built and maintained by the defendant. At trial it was held that although the defendant owed a duty of care to entrants, a duty was not owed to the plaintiff. The judge found that the plaintiff was different to other entrants who used facilities provided by a council in a public park. The plaintiff was not relying upon the defendant to provide a BMX track with jumps that were reasonably safe as the evidence was that the track was regularly altered by third parties and the plaintiff knew that. Therefore it was reasoned that the plaintiff was relying upon the ability of the third parties who modified the jump and his own ability to use it, not the ability of the defendant to provide a reasonably safe track (at [10]). The trial judge also held that if a duty was owed, the defence of volenti applied so as to defeat the claim for damages. This was based upon the evidence that the plaintiff knew of the modification of the jump by third parties and knew of the risk. It was held that the plaintiff ‘had the appropriate subjective appreciation of the risk’ (at [11]).

An analysis of the variability in Queensland WiM data

The Queensland Department of Main Roads uses Weigh-in-Motion (WiM) devices to covertly monitor (at highway speed) axle mass, axle configurations and speed of heavy vehicles on the road network. Such data is critical for the planning and design of the road network. Some of the data appears excessively variable. The current work considers the nature, magnitude and possible causes of WiM data variability. Over fifty possible causes of variation in WiM data have been identified in the literature. Data exploration has highlighted five basic types of variability specifically: ----- • cycling, both diurnal and annual;----- • consistent but unreasonable data;----- • data jumps;----- • variations between data from opposite sides of the one road; and ----- • non-systematic variations.----- This work is part of wider research into procedures to eliminate or mitigate the influence of WiM data variability.

Symmetry of in-shoe force signatures in athletes under field conditions : an application for injury prevention

The aetiology behind overuse injuries such as stress fractures is complex and multi-factorial. In sporting events where the loading is likely to be uneven (e.g. hurdling and jumps), research has suggested that the frequency of stress fractures seems to favour the athlete’s dominant limb. The tendency for an individual to have a preferred limb for voluntary motor acts makes limb selection a possible factor behind the development of unilateral overuse injuries, particularly when repeatedly used during high loading activities. The event of sprint hurdling is well suited for the study of loading asymmetry as the hurdling technique is repetitive and the limb movement asymmetrical. Of relevance to this study is the high incidence of Navicular Stress Fractures (NSF) in hurdlers, with suggestions there is a tendency for the fracture to develop in the trail leg foot, although this is not fully accepted. The Ground Reaction Force (GRF) with each foot contact is influenced by the hurdle action, with research finding step-to-step loading variations. However, it is unknown if this loading asymmetry extends to individual forefoot joints, thereby influencing stress fracture development. The first part of the study involved a series of investigations using a commercially available matrix style in-shoe sensor system (FscanTM, Tekscan Inc.). The suitability of insole sensor systems and custom made discrete sensors for use in hurdling-related training activities was assessed. The methodology used to analyse foot loading with each technology was investigated. The insole and discrete sensors systems tested proved to be unsuitable for use during full pace hurdling. Instead, a running barrier task designed to replicate the four repetitive foot contacts present during hurdling was assessed. This involved the clearance of a series of 6 barriers (low training hurdles), place in a straight line, using 4 strides between each. The second part of the study involved the analysis of "inter-limb" and "within foot loading asymmetries" using stance duration as well as vertical GRF under the Hallux (T1), the first metatarsal head (M1) and the central forefoot peak pressure site (M2), during walking, running, and running with barrier clearances. The contribution to loading asymmetry that each of the four repetitive foot contacts made during a series of barrier clearances was also assessed. Inter-limb asymmetry, in forefoot loading, occurred at discrete forefoot sites in a non-uniform manner across the three gait conditions. When the individual barrier foot contacts were compared, the stance duration was asymmetrical and the proportion of total forefoot load at M2 was asymmetrical. There were no significant differences between the proportion of forefoot load at M1, compared to M2; for any of the steps involved in the barrier clearance. A case study testing experimental (discrete) sensors during full pace sprinting and hurdling found that during both gait conditions, the trail limb experienced the greater vertical GRF at M1 and M2. During full pace hurdling, increased stance duration and vertical loading was a characteristic of the trail limb hurdle foot contacts. Commercially available in-shoe systems are not suitable for on field assessment of full pace hurdling. For the use of discrete sensor technology to become commonplace in the field, more robust sensors need to be developed.

Post-match changes in neuromuscular function and the relationship to match demands in amateur rugby league matches

Objectives: The current study investigated the change in neuromuscular contractile properties following competitive rugby league matches and the relationship with physical match demands. Design: Eleven trained, male rugby league players participated in 2–3 amateur, competitive matches (n = 30). Methods: Prior to, immediately (within 15-min) and 2 h post-match, players performed repeated counter-movement jumps (CMJ) followed by isometric tests on the right knee extensors for maximal voluntary contraction (MVC), voluntary activation (VA) and evoked twitch contractile properties of peak twitch force (Pt), rate of torque development (RTD), contraction duration (CD) and relaxation rate (RR). During each match, players wore 1 Hz Global Positioning Satellite devices to record distance and speeds of matches. Further, matches were filmed and underwent notational analysis for number of total body collisions. Results: Total, high-intensity, very-high intensity distances covered and mean speed were 5585 ± 1078 m, 661 ± 265, 216 ± 121 m and 75 ± 14 m min−1, respectively. MVC was significantly reduced immediately and 2 h post-match by 8 ± 11 and 12 ± 13% from pre-match (p < 0.05). Moreover, twitch contractile properties indicated a suppression of Pt, RTD and RR immediately post-match (p < 0.05). However, VA was not significantly altered from pre-match (90 ± 9%), immediately-post (89 ± 9%) or 2 h post (89 ± 8%), (p > 0.05). Correlation analyses indicated that total playing time (r = −0.50) and mean speed (r = −0.40) were moderately associated to the change in post-match MVC, while mean speed (r = 0.35) was moderately associated to VA. Conclusions: The present study highlights the physical demands of competitive amateur rugby league result in interruption of peripheral contractile function, and post-match voluntary torque suppression may be associated with match playing time and mean speeds.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

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.

Informational constraints on performance of dynamic interceptive actions

Utilising quantitative and qualitative research methods the thesis explored how movement patterns were coordinated under different conditions in elite athletes. Results revealed each elite athlete's ability to use multiple, varied information sources to guide successful task performance, highlighting the specific role of surrounding objects in the performance environment to perceptually guide behaviour. Combining elite coaching knowledge with empirical research enhanced understanding of the role of vision in regulating interceptive behaviours, enhancing the representative design of training environments. The main findings have been applied to training design of the Athletics Australia National Jumps Centre at the Queensland Academy of Sport in preparation for the World Indoor Championships, World Championships, and Olympic Games for Australian long and triple jumpers.

Universal codes from switching strategies

We discuss algorithms for combining sequential prediction strategies, a task which can be viewed as a natural generalisation of the concept of universal coding. We describe a graphical language based on Hidden Markov Models for defining prediction strategies, and we provide both existing and new models as examples. The models include efficient, parameterless models for switching between the input strategies over time, including a model for the case where switches tend to occur in clusters, and finally a new model for the scenario where the prediction strategies have a known relationship, and where jumps are typically between strongly related ones. This last model is relevant for coding time series data where parameter drift is expected. As theoretical contributions we introduce an interpolation construction that is useful in the development and analysis of new algorithms, and we establish a new sophisticated lemma for analysing the individual sequence regret of parameterised models.

Power transfer and mode transitions in low-frequency inductively coupled plasmas

Operation and mode jumps in low-frequency (500 kHz) radio-frequency inductively coupled plasmas are investigated. The discharge is driven by a flat inductive coil which can excite the electrostatic (E) and electromagnetic (H) discharge modes. The power transfer efficiency and mode transition behavior are studied. It is found that the power reflection coefficient as a function of the input power is minimal in the vicinity of the mode transitions and exhibits hysteresis, which is also observed when the operating gas pressure is varied.

Further development of discrete computational techniques for calculation of restricted diffusion propagators in porous media

Magnetic resonance is a well-established tool for structural characterisation of porous media. Features of pore-space morphology can be inferred from NMR diffusion-diffraction plots or the time-dependence of the apparent diffusion coefficient. Diffusion NMR signal attenuation can be computed from the restricted diffusion propagator, which describes the distribution of diffusing particles for a given starting position and diffusion time. We present two techniques for efficient evaluation of restricted diffusion propagators for use in NMR porous-media characterisation. The first is the Lattice Path Count (LPC). Its physical essence is that the restricted diffusion propagator connecting points A and B in time t is proportional to the number of distinct length-t paths from A to B. By using a discrete lattice, the number of such paths can be counted exactly. The second technique is the Markov transition matrix (MTM). The matrix represents the probabilities of jumps between every pair of lattice nodes within a single timestep. The propagator for an arbitrary diffusion time can be calculated as the appropriate matrix power. For periodic geometries, the transition matrix needs to be defined only for a single unit cell. This makes MTM ideally suited for periodic systems. Both LPC and MTM are closely related to existing computational techniques: LPC, to combinatorial techniques; and MTM, to the Fokker-Planck master equation. The relationship between LPC, MTM and other computational techniques is briefly discussed in the paper. Both LPC and MTM perform favourably compared to Monte Carlo sampling, yielding highly accurate and almost noiseless restricted diffusion propagators. Initial tests indicate that their computational performance is comparable to that of finite element methods. Both LPC and MTM can be applied to complicated pore-space geometries with no analytic solution. We discuss the new methods in the context of diffusion propagator calculation in porous materials and model biological tissues.

A directed continuous time random walk model with jump length depending on waiting time

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x,t) of finding the walker at position at time is completely determined by the Laplace transform of the probability density function φ(t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.

Volatility transmission in global financial markets

This paper considers the transmission of volatility in global foreign exchange, equity and bond markets. Using a multivariate GARCH framework which includes measures of realised volatility as explanatory variables, significant volatility and news spillovers are found to occur on the same trading day between Japan, Europe, and the United States. All markets exhibit significant degrees of asymmetry in terms of the transmission of volatility associated with good and bad news. There are also strong links between diffusive volatilities in all three markets, whereas jumpactivity is only importantwithin the equitymarkets. The results of this paper deepen our understanding of how news and volatility are propagated through global financial markets.

Estimating the parameters of stochastic volatility models using option price data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.

Stochastic growth models for analyzing crustacean data

The contemporary methodology for growth models of organisms is based on continuous trajectories and thus it hinders us from modelling stepwise growth in crustacean populations. Growth models for fish are normally assumed to follow a continuous function, but a different type of model is needed for crustacean growth. Crustaceans must moult in order for them to grow. The growth of crustaceans is a discontinuous process due to the periodical shedding of the exoskeleton in moulting. The stepwise growth of crustaceans through the moulting process makes the growth estimation more complex. Stochastic approaches can be used to model discontinuous growth or what are commonly known as "jumps" (Figure 1). However, in stochastic growth model we need to ensure that the stochastic growth model results in only positive jumps. In view of this, we will introduce a subordinator that is a special case of a Levy process. A subordinator is a non-decreasing Levy process, that will assist in modelling crustacean growth for better understanding of the individual variability and stochasticity in moulting periods and increments. We develop the estimation methods for parameter estimation and illustrate them with the help of a dataset from laboratory experiments. The motivational dataset is from the ornate rock lobster, Panulirus ornatus, which can be found between Australia and Papua New Guinea. Due to the presence of sex effects on the growth (Munday et al., 2004), we estimate the growth parameters separately for each sex. Since all hard parts are shed too often, the exact age determination of a lobster can be challenging. However, the growth parameters for the aforementioned moult processes from tank data being able to estimate through: (i) inter-moult periods, and (ii) moult increment. We will attempt to derive a joint density, which is made up of two functions: one for moult increments and the other for time intervals between moults. We claim these functions are conditionally independent given pre-moult length and the inter-moult periods. The variables moult increments and inter-moult periods are said to be independent because of the Markov property or conditional probability. Hence, the parameters in each function can be estimated separately. Subsequently, we integrate both of the functions through a Monte Carlo method. We can therefore obtain a population mean for crustacean growth (e. g. red curve in Figure 1). [GRAPHICS]