RAROC-Based contingent claim valuation

University of Technology Sydney. Faculty of Business.The present dissertation investigates the valuation of a contingent claim based on the criterion RAROC, an abbreviation of Risk-Adjusted Return on Capital. RAROC is defined as the ratio of expected return to risk, and may therefore be regarded as a performance measure. RAROC-based pricing theory can indeed be considered as a subclass of the broader `good-deal' pricing theory, developed by Bernardo and Ledoit (2000) and Cochrane and Saá-Requejo (2000). By fixing some specific target value of RAROC, a RAROC-based good-deal price for a contingent claim is determined as follows: upon charging the counterparty with this price and using available funds, we are able to construct a hedging portfolio such that the maximum achievable RAROC of our hedged position meets the target RAROC. As a first step, we consider the standard Black-Scholes model, but allow only static hedging strategies. Assuming that the contingent claim in question is a call option, we examine the behavior of maximum value of RAROC as a function of initial call price, as well as the corresponding optimal static hedging strategy. In this analysis we consider two specifications for the risk component of RAROC, namely Value-at-Risk and Expected Shortfall. Subsequently, we allow continuous-time trading strategies, while remaining in the Black-Scholes framework. In this case we suppose that the initial price of the call option is limited to be below the Black-Scholes price. Perfect hedging is thus impossible, and the position must contain some residual risk. For ease of analysis, we restrict our attention to a specific class of hedging strategies and examine the maximum RAROC for each strategy in this class. In the interest of tractability, the version of RAROC adopted risk is measured simply as expected loss. While the previous approach only permits us to examine the constrained maximum RAROC over a specific class of hedging strategies, we would like to employ a more general method in order to study the global maximum RAROC over all hedging strategies. To do so, we introduce the notion of dynamic RAROC-based good-deal prices. In particular, with reference to the dynamic good-deal pricing theory of Becherer (2009), such prices are required to satisfy certain dynamic conditions, so that inconsistent decision-making between different times can be avoided. This task is accomplished by constructing prices that behave like time-consistent dynamic coherent risk measures. As soon as the construction process is finished, we set up a discrete time incomplete market, and demonstrate how to determine the dynamic RAROC-based good-deal price for a call option. Furthermore, by following Becherer (2009), we derive the dynamics of RAROC-based good-deal prices as solutions for discrete-time backward stochastic difference equations. Finally, we introduce RAROC-based good-deal hedging strategies, and examine their representation in terms of discrete-time backward stochastic difference equations

Design of a regional climate model for the simulation of South China summer monsoon rainfall

The objective of this study is to modify a regional climate model (RCM)-the Regional Climate Model of the National Climate Center of China-to simulate the summer monsoon rainfall over South China and the South China Sea. Such a modification is necessary because this RCM was designed for studying the climate over central and north China where precipitation processes are very different from those occurring further south so that simulations using the basic parameters of the original model give precipitation amounts much less than those observed. Using the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis data, many sensitivity experiments have been carried out for the months of April to June 1998, which include modifying the cumulus parameterization scheme, the large-scale precipitation scheme, the radiation scheme, the surface exchange processes, and the size of the buffer zone. The design of all the experiments is either to enhance the moisture provision to the atmosphere over South China and the South China Sea, or to help the model atmosphere realize the moisture to form precipitation. It is found that indeed modifications to the various parameters can produce rainfall amounts much closer to those observed. Based on the results of these experiments, an "optimal" design of the RCM is reached and tested for its effectiveness using the NCEP reanalyses for two wet years (1994 and 1997) and two dry years (1996 and 1999) during which rainfall in May and June over South China were above/below normal respectively. The physical processes in this design include the Kuo scheme for convective precipitation, the Pal scheme for large-scale precipitation, the Holtslag scheme for the planetary boundary layer, the radiation transfer scheme of the NCAR Community Climate Model Version 3, and the Biosphere-Atmosphere Transfer Scheme for the land surface process. The width of the buffer zone is reduced and the effective cloud droplet radius is fixed at different values over land and ocean. The neutral drag coefficient is prescribed as a function of surface wind speed, and the heat and moisture exchange coefficients are set at values larger than that of momentum. The simulations based on this design for all the five years are found to be much closer to observations than those from the control

Extended MULTIMOORA method based on Shannon entropy weight for materials selection

Selection of appropriate material is a crucial step in engineering design and manufacturing process. Without a systematic technique, many useful engineering materials may be ignored for selection. The category of multiple attribute decision-making (MADM) methods is an effective set of structured techniques. Having uncomplicated assumptions and mathematics, the MULTIMOORA method as an MADM approach can be effectively utilized for materials selection. In this paper, we developed an extension of MULTIMOORA method based on Shannon entropy concept to tackle materials selection process. The entropy concept was considered to assign relative importance to decision-making attributes. The proposed model consists of two scenarios named the weighted and entropyweighted MULTIMOORA methods. In the first scenario, subjective weight was considered in the formulation of the approach like most of conventional MADM methods. The general form of entropy weight that is a combination of subjective and objective weighting factors was employed for the second scenario. We examined two popular practical examples concerning materials selection to show the application of the suggested approach and to reveal the effect of entropy weights. Our results were compared with the earlier studies

Thirty-day mortality following surgical management of hip fractures during the COVID-19 pandemic: findings from a prospective multi-centre UK study

Purpose Thirty-day mortality of patients with hip fracture is well researched and predictive; validated scoring tools have been developed (Nottingham Hip Fracture Score, NHFS). COVID-19 has significantly greater mortality in the elderly and comorbid patients which includes hip fracture patients. Non-operative treatment is not appropriate due to significantly higher mortality, and therefore, these patients are often exposed to COVID-19 in the peri-operative period. What is unclear is the effect of concomitant COVID-19 infection in these patients. Methods A multicentre prospective study across ten sites in the United Kingdom (responsible for 7% of hip fracture patients per annum in the UK). Demographic and background information were collected by independent chart review. Data on surgical factors included American Society of Anesthesiologists (ASA) score, time to theatre, Nottingham Hip fracture score (NHFS) and classification of fracture were also collected between 1st March 2020 and 30th April 2020 with a matched cohort from the same period in 2019. Results Actual and expected 30-day mortality was found to be significantly higher than expected for 2020 COVID-19 positive patients (RR 3.00 95% CI 1.57–5.75, p < 0.001), with 30 observed deaths compared against the 10 expected from NHFS risk stratification. Conclusion COVID-19 infection appears to be an independent risk factor for increased mortality in hip fracture patients. Whilst non-operative management of these fractures is not suggested due to the documented increased risks and mortality, this study provides evidence to the emerging literature of the severity of COVID-19 infection in surgical patients and the potential impact of COVID-19 on elective surgical patients in the peri-operative period