Pricing of contingent claims under the real-world measure

University of Technology, Sydney. Faculty of Science.The aim of this thesis is to price contingent claims under the real-world probability measure. Real-world pricing results naturally by selecting the numeraire as the growth optimal portfolio (GOP). Under this approach, the existence of an equivalent risk-neutral probability measure is not required. Furthermore, the GOP can be used to define other basic contingent claims, such as exchange prices, primary security accounts, and even zero-coupon bonds. We begin with application of the real-world pricing formula to derive forward prices for each of these financial quantities. The obtained formulae are model independent, yet reveal important differences between the real-world arid classical risk-neutral approaches. Real-world prices are systematically derived under each of the models studied within this thesis for the following contingent claims: zero-coupon bonds; options on the GOP: options on exchange prices; and interest rate caps and floors via options on zero-coupon bonds. We start with the classic Black-Scholes-Merton model, where the GOP follows a geometric Brownian motion. Under this model, real-world pricing recovers the results of classical risk-neutral pricing, since the corresponding Radon-Nikodym derivative is a martingale. For each of the remaining models studied, the GOP is based on a time-transformed squared Bessel process. In each case, real-world prices may differ from classical risk-neutral prices because the candidate Radon-Nikodym derivative is a strict supermartingale. The second model considered proposes a modified form of the constant elasticity of variance model for the GOP. New analytic results for zero- coupon bonds and options on the GOP are derived that were previously analysed using numerical methods. Real-world prices for options on exchange prices and interest rate derivatives are also provided. Three versions of the minimal market model are also examined. This model class overcomes some of the deficiencies of the aforementioned approaches since the dynamics for the GOP better reflect empirical market features, such as leptokurtic returns, the leverage effect and a stochastic yet stationary volatility structure. Under a stylised version of the minimal market model with a constant short rate, we derive analytic solutions to the complete suite of contingent claims examined within the thesis. We subsequently allow the short rate to be stochastic in order to accurately model the term structure of interest rates, with a focus on low interest rate environments. The proposed model provides a very good fit to interest rate

Analytic pricing of contingent claims under the real-world measure

This article derives a series of analytic formulae for various contingent claims under the real-world probability measure using the stylised minimal market model (SMMM). This model provides realistic dynamics for the growth optimal portfolio (GOP) as a well-diversified equity index. It captures both leptokurtic returns with correct tail properties and the leverage effect. Under the SMMM, the discounted GOP takes the form of a time-transformed squared Bessel process of dimension four. From this property, one finds that the SMMM possesses a special and interesting relationship to non-central chi-square random variables with zero degrees of freedom. The analytic formulae derived under the SMMM include options on the GOP, options on exchange prices and options on zero-coupon bonds. For options on zero-coupon bonds, analytic prices facilitate efficient calculation of interest rate caps and floors. © 2008 World Scientific Publishing Company

Point‐of‐care lung ultrasound in patients with COVID‐19 – a narrative review

Ultrasound imaging of the lung and associated tissues may play an important role in the management of patients with COVID‐19–associated lung injury. Compared with other monitoring modalities, such as auscultation or radiographic imaging, we argue lung ultrasound has high diagnostic accuracy, is ergonomically favourable and has fewer infection control implications. By informing the initiation, escalation, titration and weaning of respiratory support, lung ultrasound can be integrated into COVID‐19 care pathways for patients with respiratory failure. Given the unprecedented pressure on healthcare services currently, supporting and educating clinicians is a key enabler of the wider implementation of lung ultrasound. This narrative review provides a summary of evidence and clinical guidance for the use and interpretation of lung ultrasound for patients with moderate, severe and critical COVID‐19–associated lung injury. Mechanisms by which the potential lung ultrasound workforce can be deployed are explored, including a pragmatic approach to training, governance, imaging, interpretation of images and implementation of lung ultrasound into routine clinical practice

Dynamic variation of supernatant quality in a dairy shed waste stabilisation pond system

An intensive monitoring program of a standard two-stage dairy shed waste stabilisation pond system was undertaken to determine the incidence and extent of spatial and temporal variation of basic physio-chemical parameters, and to shed light on the longer term dynamic nature of in-pond conditions. The anaerobicâfacultative pond system, located in a remote rural area, treats wastewater from the hosing down and hydraulic flushing of the milking parlour and holding yard at the farm dairy shed. A number of multi-parameter water quality field monitoring probes were permanently deployed at various locations within the two ponds to enable continuous measurement of temperature, pH, conductivity and dissolved oxygen. In addition, profiling of the supernatant of both ponds was undertaken at different times of the year to examine vertical variation of the same parameters. Continuous monitoring revealed spatial homogeneity in EC and pH levels in the upper metre of both ponds. Physio-chemical parameters also appear to change uniformly across the ponds in response to external stimuli such as rainfall. Neither pond, however, exhibits homogeneity down the profile of the supernatant. Seasonal stratification is prevalent in the facultative pond suggesting poor vertical mixing, while the anaerobic pond is notably affected by sludge accumulation. A long-term pattern of rising conductivity in both ponds indicated accumulation of dissolved salt species in the system due to recirculation of reclaimed effluent for hydraulic flushing of the dairy shed. In the facultative pond, diurnal fluctuations in dissolved oxygen, oxidation-reduction potential and turbidity during warmer months of the year closely followed temperature swings. The extensive data collected in this study provides a detailed picture of the physio-chemical dynamics of two-stage stabilisation pond systems treating dairy shed wastewater

Physical and hydrodynamic characteristics of a dairy shed waste stabilisation pond system

Waste stabilization pond systems are widely used to treat animal wastes under highly variable hydraulic loading regimes. These systems have received limited research attention with regard to their hydrodynamic behaviour and the potential impact of shock hydraulic loading on their performance. In this study a two-stage dairy shed waste stabilisation pond system was topographically surveyed to determine the physical shape and the theoretical hydraulic retention time (HRT) of each pond, as well as the extent of sludge accumulation in the primary pond. The primary pond was then subjected to a series of drogue tracking runs whereby weighted floating survey targets with submerged âsailsâ were tracked during their movement through the pond at times of peak flow in order to characterise the hydrodynamic behaviour of the pond. The full capacity volumes of the primary and secondary ponds were calculated to be 1285m3 and 2391m3, respectively. Sludge had been accumulating in the primary pond at a rate of 0.73m3/d over a period of 2.4 years and this has reduced the active treatment volume of the pond to 657m3. Based on mean outflow, the HRTs of the ponds were 40 d and 137 d, respectively. The drogue runs revealed a vortexlike mixing pattern within the pond with higher velocities around the perimeter of the pond between the inlet and outlet, and lower velocities in the centre of the pond. In-pond velocities seemed relatively high in comparison with those from other drogue studies of larger ponds and the surging inflow caused the formation of a flow âjetâ that potentially contributed to significant short-circuiting. The range of influence of this flow jet, however, was limited to within 15m of the inlet, suggesting that short-circuiting would be likely to occur only under certain high inflow conditions

Assessment of GFR by four methods in adults in Ashanti, Ghana: the need for an eGFR equation for lean African populations

Background. Equations for estimating glomerular filtration rate (GFR) have not been validated in Sub-Saharan African populations, and data on GFR are few. Methods. GFR by creatinine clearance (Ccr) using 24-hour urine collections and estimated GFR (eGFR) using the four-variable Modification of Diet in Renal Disease (MDRD-4)[creatinine calibrated to isotope dilution mass spectrometry (IDMS) standard], Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Cockcroft–Gault equations were obtained in Ghanaians aged 40–75. The population comprised 1013 inhabitants in 12 villages; 944 provided a serum creatinine and two 24-hour urines. The mean weight was 54.4 kg; mean body mass index was 21.1 kg/m2. Results. Mean GFR by Ccr was 84.1 ml/min/1.73m2; 86.8% of participants had a GFR of 60 ml/min/1.73m2. Mean MDRD-4 eGFR was 102.3 ml/min/1.73m2 (difference vs. Ccr, 18.2: 95% CI: 16.8–19.5); when the factor for black race was omitted, the value (mean 84.6 ml/min/1.73m2) was close to Ccr. Mean CKD-EPI eGFR was 103.1 ml/min/1.73m2, and 89.4 ml/min/1.73m2 when the factor for race was omitted. The Cockcroft–Gault equation underestimated GFR compared with Ccr by 9.4 ml/min/1.73m2 (CI: 8.3–10.6); particularly in older age groups. GFR by Ccr, and eGFR by MDRD-4, CKD-EPI and Cockcroft–Gault showed falls with age: MDRD-4 5.5, Ccr 7.7, CKD-EPI 8.8 and Cockcroft–Gault 11.0 ml/min/1.73m2/10 years. The percentage of individuals identified with CKD stages 3–5 depended on the method used: MDRD-4 1.6% (7.2 % without factor for black race; CKD-EPI 1.7% (4.7% without factor for black race), Ccr 13.2% and Cockcroft–Gault 21.0%. Conclusions. Mean eGFR by both MDRD-4 and CKD-EPI was considerably higher than GFR by Ccr and Cockcroft–Gault, a difference that may be attributable to leanness. MDRD-4 appeared to underestimate the fall in GFR with age compared with the three other measurements; the fall with CKD-EPI without the adjustment for race was the closest to that of Ccr. An equation tailored specifically to the needs of the lean populations of Africa is urgently needed. For the present, the CKD-EPI equation without the adjustment for black race appears to be the most useful

Pacheco and Charanga: imitation, innovation and cultural appropriation in the típico tradition of New York City

Abstract In this article the performance practice of Afro-Cuban dance music is explored and discourses surrounding creativity brought to bear on questions surrounding innovation and stylistic development. A case study of Dominican-born Johnny Pacheco, charanga flute player and co-creator of the term ‘salsa,’ enables issues including imitation, innovation and cultural appropriation to be explored within the context of típico charanga performance in mid-twentieth-century New York