The Great Financial Crisis (GFC) of 2008 left many financial institutions devastated. Despite the practice of advanced risk management at the time, society witnessed the collapse of the “too big to fail” institutions. Gaping holes within the existing risk framework lurked, which both regulators and practitioners failed to detect. This dissertation discusses the symptoms of the crisis that were overlooked and explores the financial engineering implemented post-2008 to avoid the next crisis. The author considers the work of Hull, White, Gregory, Brigo, Kenyon, Green, Morini, Pallavicini, Piterbarg, Burgard, Kjaer, Elouerkhaoui, and Castagna. A literature review is provided for each of the mentioned names to highlight each author’s contribution to the field of Total Value Adjustment (XVA) pricing. An in-depth analysis on the funding invariance principle suggested by Elouerkhaoui is provided followed by a model implementation. The core aim of this dissertation is to review XVA valuations from a practitioners perspective using the framework provided by Elouerkhaoui. A secondary aim of the dissertation is to briefly explore the work of Aboura and Maillard on the Cornish-Fisher Transformation (CF). The CF is considered as a parsimonious approach in estimating non-normal distributions, therefore an interesting alternative to price XVA using Monte Carlo (MC) simulation. / Dissertation (MSc)--University of Pretoria, 2017. / Mathematics and Applied Mathematics / MSc / Unrestricted

Total valuation adjustment (XVA) is a new technique which takes multiple material financial factors into consideration when pricing derivatives. This paper explores how funding costs and counterparty credit risk affect pricing the American option based on no-arbitrage analysis. We review previous studies of European option pricing with different funding costs. The conclusions help to compute the no- arbitrage price of the American option in the model with different borrowing and lending rates. Another model with counterparty credit risk is set up, and this pricing approach is referred to as credit valuation adjustment (CVA). A defaultable bond issued by the counterparty is used to hedge the loss from the option's default. We incorporate these two models to assess the XVA of an American option. The collateral, which protects the option investors from default, is considered in our benchmark model. To illustrate our results, numerical experiments are designed to demonstrate the relationship between XVA and parameters, which include the funding rates, bond's rate of return, and number of periods.

This paper aims to calculate the all-inclusive European option price based on XVA model numerically. For European type options, the XVA can be calculated as so- lution of a BSDE with a specific driver function. We use the FT scheme to find a linear approximation of the nonlinear BSDE and then use linear regression Monte Carlo method to calculate the option price.

Development of hair cell stereocilia bundles involves three stages: elongation, thickening, and supernumerary stereocilia retraction. Although Myo-XVa is known to be essential for stereocilia elongation, its role in retraction/thickening remains unknown. We quantified stereocilia numbers/diameters in shaker-2 mice (Myo15sh2) that have deficiencies in “long” and “short” isoforms of myosin-XVa, and in mice lacking only the “long” myosin-XVa isoform (Myo15ΔN). Our data showed that myosin-XVa is largely not involved in the developmental retraction of supernumerary stereocilia. In normal development, the diameters of the first (tallest)/second row stereocilia within a bundle are equal and grow simultaneously. The diameter of the third row stereocilia increases together with that of taller stereocilia until P1-2 and then either decreases almost two-fold in inner hair cells (IHCs) or stays the same in outer hair cells (OHCs), resulting in a prominent diameter gradation in IHCs and less prominent in OHCs. Sh2 mutation abolishes this gradation in IHCs/OHCs. Stereocilia of all rows grow in diameters nearly equally in Myo15sh2/sh2 IHCs and OHCs. Conversely, ΔN mutation does not affect normal stereocilia diameter gradation until ~P8. Therefore, myosin-XVa “short” isoform is essential for developmental thinning of third row stereocilia, which causes diameter gradation within a hair bundle.