On spatially irregular ordinary differential equations and a pathwise volatility modelling framework

This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's squared volatility. In the new framework, corresponding processes are strictly increasing, solve random ODEs, and are composed with geometric Brownian motion to obtain price processes. The new framework has no dependence on stochastic calculus, so processes can be studied on a pathwise basis using probability-free ODE techniques and functional analysis. The ODEs considered depend on continuous driving functions which are `spatially irregular', meaning they need not have any spatial regularity properties such as Holder continuity. They are however strictly increasing in time, thus temporally asymmetric. When sensible initial values are chosen, IVP solutions are also strictly increasing, and the IVPs' solution set is shown to contain all differentiable bijections on the non-negative reals. This enables the modelling of any non-negative volatility path which is not zero over intervals, via the time derivative of solutions. Despite this generality, new well-posedness results establish the uniqueness of solutions going forwards in time, and continuity of the IVPs' solution map. Motivation to explore this framework comes from its connection with the Heston volatility model. The framework explains how Heston price processes can converge to an interval-valued generalisation of the NIG Levy process, and reveals a deeper relationship between integrated CIR processes and the IG Levy process. Within this framework, a `Riemann-Liouville-Heston' martingale model is defined which generalises these relationships to fractional counterparts. Implied volatilities from this model are simulated, and exhibit features characteristic of leading `rough' volatility models.Comment: The author's PhD thesis. Major extension of v2. 211 pages, 22 figure

Fluid or fuel? The context of consuming a beverage is important for satiety

Energy-containing beverages have a weak effect on satiety, limited by their fluid characteristics and perhaps because they are not considered ‘food’. This study investigated whether the context of consuming a beverage can influence the satiating power of its nutrients. Eighty participants consumed a lower- (LE, 75 kcal) and higher-energy (HE, 272 kcal) version of a beverage (covertly manipulated within-groups) on two test days, in one of four beverage contexts (between-groups): thin versions of the test-drinks were consumed as a thirst-quenching drink (n = 20), a filling snack (n = 20), or without additional information (n = 20). A fourth group consumed subtly thicker versions of the beverages without additional information (n = 20). Lunch intake 60 minutes later depended on the beverage context and energy content (p = 0.030): participants who consumed the thin beverages without additional information ate a similar amount of lunch after the LE and HE versions (LE = 475 kcal, HE = 464 kcal; p = 0.690) as did those participants who believed the beverages were designed to quench-thirst (LE = 442 kcal, HE = 402 kcal; p = 0.213), despite consuming an additional 197 kcal in the HE beverage. Consuming the beverage as a filling snack led participants to consume less at lunch after the HE beverage compared to the LE version (LE = 506 kcal, HE = 437 kcal; p = 0.025). This effect was also seen when the beverages were subtly thicker, with participants in this group displaying the largest response to the beverage’s energy content, consuming less at lunch after the HE version (LE = 552 kcal, HE = 415 kcal; p<0.001). These data indicate that beliefs about the consequences of consuming a beverage can affect the impact of its nutrients on appetite regulation and provide further evidence that a beverage’s sensory characteristics can limit its satiating power

Optimising foods for satiety

Foods that generate strong satiety sensations have obvious ben- efits for weight management. This review builds on the under- standing that a food’s satiating power is dependent on the amount of protein, carbohydrate, fat and fibre it contains by examining evidence that the consumer’s sensory and cognitive appraisal of the food is also important. It is concluded that numerous features of a food product can be manipulated to enhance the consumer’s experience of satiety but the combi- nation of these features will ultimately determine its effect on appetite control. Taking this integrated approach to satiety will optimise the development of high satiety foods

Optimising beverages for satiety: the role of sensory characteristics, expectations and nutrient content

Regularly consuming caloric beverages has been linked to obesity and weight gain and evidence suggests this is because beverages have a weak impact on satiety responses (behavioural and physiological). Using a series of experimental studies this thesis explored the cognitive and sensory features of caloric beverages that might enhance the anticipated and actual satiating power of their nutrients. Paper one characterised the sensory characteristics associated with expectations of hunger, fullness and thirst, finding that food and beverage products anticipated to be creamier and thicker were expected to be more satiating and less thirst-quenching. Paper two established that people can perceive subtle changes in beverage viscosity and manipulating thick and creamy textural cues strongly influenced the expectation that a beverage would be filling and supress hunger after consumption. This was extended in paper three, which reported evidence suggesting that a sensorially enhanced beverage is selected and consumed in smaller portions. Papers four and five investigated the satiating power of a caloric beverage consumed with satiety-relevant cognitive and sensory information. Paper four reported tentative evidence that a labelled satiety message influenced the satiating effect of caloric beverages when combined with thick and creamy sensory cues. Participants in Paper five reported greater satiety responses to a covert manipulation of beverage energy when consumed as a ‘snack’ rather than a drink. However, consuming the same beverage in a subtly thicker sensory context (without extra information) generated the largest satiety response to the different nutrient loads, perhaps because textural characteristics are the most reliable cue for nutrients. Overall these studies suggest that caloric beverages may generate weak satiety responses because their nutrient-generated effects are not expected. Encouraging people to consider caloric beverages as a snack, or adding in nutrient-relevant sensory characteristics, may both help consumers regulate energy intake when consuming these products

Turbocharging Monte Carlo pricing for the rough Bergomi model

The rough Bergomi model, introduced by Bayer, Friz and Gatheral [Quant. Finance 16(6), 887-904, 2016], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in equity markets. In the absence of analytical European option pricing methods for the model, we focus on reducing the runtime-adjusted variance of Monte Carlo implied volatilities, thereby contributing to the model's calibration by simulation. We employ a novel composition of variance reduction methods, immediately applicable to any conditionally log-normal stochastic volatility model. Assuming one targets implied volatility estimates with a given degree of confidence, thus calibration RMSE, the results we demonstrate equate to significant runtime reductions - roughly 20 times on average, across different correlation regimes

Effects of repeated consumption on sensory-enhanced satiety

Previous research suggests that sensory characteristics of a drink modify the acute satiating effects of its nutrients, with enhanced satiety evident when a high energy drink was thicker and tasted creamier. The present study tested whether this modulation of satiety by sensory context was altered by repeated consumption. Participants (n=48) consumed one of four drinks mid-morning on seven non-consecutive days with satiety responses measured pre-exposure (day 1), post-exposure (day 6) and at a one month follow-up. Drinks combined two levels of energy (lower energy, LE, 326 KJ: higher energy, HE, 1163KJ) with two levels of satiety-predictive sensory characteristics (low-sensory, LS, or enhanced sensory, ES). Test lunch intake 90 minutes after drink consumption depended on both the energy content and sensory characteristics of the drink before exposure, but on energy content alone at post-exposure and the follow-up. The largest change was an increase in test meal intake over time in the LE/LS condition. Effects on intake were reflected in appetite ratings, with rated hunger and expected filling affected by sensory characteristics and energy content pre-exposure, but were largely determined by energy content post exposure and at follow up. In contrast, a measure of expected satiety reflected sensory characteristics regardless of energy content on all three test days. Overall these data suggest that some aspects of the sensory-modulation of satiety are changed by repeated consumption, with covert energy becoming more effective in suppressing appetite over time, but also suggest that these behavioural changes are not readily translated into expectations of satiety

Expectations about satiety and thirst are modified by acute motivational state

Prior research has shown that consumers have clear and measurable expectations about the likely effects of food and drink items on their appetite and thirst, which are acquired with experience and influenced by a product’s taste and texture. What is unclear is whether expression of these expectations also varies with current appetitive state. It is possible that current appetite could increase or decrease the relevance of these expectations for future food choice and magnify a product’s expected impact on appetite. To test this, we contrasted expectations about satiety and thirst for four products consumed two hours after an appetite manipulation at breakfast, achieved through ad libitum access to low-energy drinks only (hunger condition), cereal only but no drinks (thirst condition) or both foods and drinks (sated condition). The test products were two soups and two drinks, with a thicker and thinner version of each product type to act as positive control to ensure sensitivity in detecting differences in expectations. For satiety, the predicted differences between products were seen: soups and thicker products were expected to be more filling and to suppress subsequent hunger more than drinks and thinner products, but these differences were more pronounced in the hunger than thirsty or sated conditions. Being thirsty also enhanced expectations of how much drinks would appease immediate thirst. Overall the data show that expectations were adjusted subtly by a person’s current appetitive state, suggesting that we have mechanisms that highlight the most important features of a product at the time when it may be most beneficial to the consumer

The Holographic Stereogram

The holographic stereogram, a hologram synthesized from ordinary stereoscopic component photographs, is investigated as an alternative to classical holograms and to previous types of stereograms for three-dimensional perfect imagery. The process is partly holographic in nature, but it provides images of naturally illuminated objects, and its application is not limited by the technology of laser illumination. The pinhole camera stereogram and the fly's eye lens stereogram are also analyzed, since the principles of their operation are similar. Pinhole camera stereogram imagery is shown to have several deficiencies, among which is the necessity for small camera-object distances. The fly's eye lens is much superior, but is limited in practice by aberrations, a difficulty which the holographic stereogram overcomes. Also treated are the full-color, the focused type, and the distortionless-scaled holographic stereogram, and optical spatial filtering of holographic stereogram images. The achromatically imaged Fresnel zone plate is analyzed as a technique of very general applicability which compensates for source incoherency in two-beam type holographic arrangements. The emphasis is on physical interpretation rather than mathematical formulation. Two simple graphical mnemonics are developed for rapid analytical inspection of the effects of, respectively, temporal and spatial incoherence of the source in any achromatically imaged zone plate or Gabor in-line type holographic system. The scalar wave function approximation of physical optics is used throughout.</p

Does modifying the thick texture and creamy flavour of a drink change portion size selection and intake?

Previous research indicates that a drink's sensory characteristics can influence appetite regulation. Enhancing the thick and creamy sensory characteristics of a drink generated expectations of satiety and improved its actual satiating effects. Expectations about food also play an important role in decisions about intake, in which case enhancing the thick and creamy characteristics of a drink might also result in smaller portion size selection. In the current study forty-eight participants (24 female) completed four test days where they came into the laboratory for a fixed-portion breakfast, returning two hours later for a mid-morning drink, which they could serve themselves and consume as much as they liked. Over the test days, participants consumed an iso-energetic drink in four sensory contexts: thin and low-creamy; thin and high-creamy; thick and low-creamy; thick and high-creamy. Results indicated that participants consumed less of the thick drinks, but that this was only true of the female participants; male participants consumed the same amount of the four drinks regardless of sensory context. The addition of creamy flavour did not affect intake but the thicker drinks were associated with an increase in perceived creaminess. Despite differences in intake, hunger and fullness ratings did not differ across male and female participants and were not affected by the drinks sensory characteristics. The vast majority of participants consumed all of the drink they served themselves indicating that differences in intake reflected portion size decisions. These findings suggest women will select smaller portions of a drink when its sensory characteristics indicate that it will be satiating

Using Sensory Cues to Optimise the Satiety Value of a Reduced-Calorie Product Labelled ‘Healthier Choice’

Reformulation strategies to reduce the energy density of commonly consumed foods and beverages are intended to support weight management, but expectations generated by labelling these as ‘healthier’ alternatives can have unintended effects on the product’s sensory evaluations and consumption behaviours. We compared the impact of four different strategies for presenting a lower-calorie beverage to consumers on product perceptions, short-term appetite and energy intake. Participants (N = 112) consumed higher- (211 kcal/portion) and lower-calorie (98 kcal/portion) fixed-portion soymilks in the morning across two test days, with the lower-calorie version presented in one of four contexts varying in label information and sensory quality: (1) sensory-matched/unlabelled, (2) sensory-matched/labelled, (3) sensory-reduced (less sweet and creamy)/labelled, and (4) sensory-enhanced (sweeter and creamier)/labelled. The label was Singapore’s Healthier Choice Symbol, which also highlighted that the soymilk was lower calorie. Changes in reported appetite, ad libitum lunch intake, and self-reported intake for the rest of the text day were recorded. Results indicated that total energy intake was consistently lower on the days the lower calorie beverages were consumed, regardless of how they were presented. However, the ‘healthier choice’ label increased hunger prior to lunch and reduced the soymilks’ perceived thickness and sweetness compared to the same unlabelled version. Increasing the product’s sensory intensity successfully maintained liking, experienced sensory quality and appetite. Results suggest that food companies wanting to explicitly label product reformulations could combine messages of ‘lower calorie’ and ‘healthier choice’ with appropriate taste and texture enhancements to maintain acceptance and avoid negative effects on appetite