Stable numerical methodology for variational inequalities with application in quantitative finance and computational mechanics

Coercivity is a characteristic property of the bilinear term in a weak form of a partial differential equation in both infinite space and the corresponding finite space utilized by a numerical scheme. This concept implies \textit{stability} and \textit{well-posedness} of the weak form in both the exact solution and the numerical solution. In fact, the loss of this property especially in finite dimension cases leads to instability of the numerical scheme. This phenomenon occurs in three major families of problems consisting of advection-diffusion equation with dominant advection term, elastic analysis of very thin beams, and associated plasticity and non-associated plasticity problems. There are two main paths to overcome the loss of coercivity, first manipulating and stabilizing a weak form to ensure that the discrete weak form is coercive, second using an automatically stable method to estimate the solution space such as the Discontinuous Petrov Galerkin (DPG) method in which the optimal test space is attained during the design of the method in such a way that the scheme keeps the coercivity inherently. In this dissertation, A stable numerical method for the aforementioned problems is proposed. A stabilized finite element method for the problem of migration risk problem which belongs to the family of the advection-diffusion problems is designed and thoroughly analyzed. Moreover, DPG method is exploited for a wide range of valuing option problems under the black-Scholes model including vanilla options, American options, Asian options, double knock barrier options where they all belong to family of advection-diffusion problem, and elastic analysis of Timoshenko beam theory. Besides, The problem of American option pricing, migration risk, and plasticity problems can be categorized as a free boundary value problem which has their extra complexity, and optimization theory and variational inequality are the main tools to study these families of the problems. Thus, an overview of the classic definition of variational inequalities and different tools and methods to study analytically and numerically this family of problems is provided and a novel adjoint sensitivity analysis of variational inequalities is proposed

Essays on the informational efficiency of credit default swaps

This thesis contributes to the strand of the financial literature on credit derivatives, in particular the credit default swaps (CDS) market. We present four inter-connected studies addressing CDS market efficiency, price discovery, informed trading and the systemic nature of the CDS market. The first study explores a specific channel through which informed traders express their views on the CDS market: mergers and acquisitions (M&A) and divestitures activities. We show that information obtained by major banks while providing these investment services is impounded by CDS rates prior to the operation announcement. The run-up to M&A announcements is characterized by greater predictability of stock returns using past CDS spread data. The second study evaluates the incremental information value of CDS open interest relative to CDS spreads using a large panel database of obligors. We find that open interest helps predict CDS rate changes and stock returns. Positive open interest growth precedes the announcement of negative earnings surprises, consistent with the notion that its predictive ability is linked to the disclosure of material information. The third study measures the impact on CDS market quality of the ban on uncovered sovereign CDS buying imposed by the European Union. Using panel data models and a difference-in-differences analysis, we find that the ban helped stabilize CDS market volatility, but was in general detrimental to overall market quality. Lastly, we investigate the determinants of open interest dynamics to uncover the channels through which CDS may endanger the financial system. Although we find information asymmetry and divergence of opinions on firms’ future performance as relevant drivers of open interest, our results indicate that systematic factors play a much greater influence. The growth of open interest for different obligors co-varies in time and is pro-cyclical. Funding costs and counterparty risk also reduce dealers’ willingness to incur inventory risk; Eficiência dos mercados de Credit Default Swaps Resumo: Esta tese investiga o mercado de derivados de crédito, e em particular o mercado de credit default swaps (CDS). São apresentados quatro estudos interligados abordando temáticas relacionadas com a eficiência informacional, a existência de negociação informada no mercado de CDS, e a natureza sistémica daquele mercado. O primeiro estudo analisa a existência de negociação informada no mercado de CDS antes de operações de aquisição, fusões ou venda de ativos relevantes. A nossa análise mostra uma reação dos prémios de CDS antes do anúncio daqueles eventos, sendo em alguns casos mais imediata do que a reação dos mercados acionistas. O segundo estudo avalia o conteúdo informativo das posições em aberto no mercado de CDS utilizando dados em painel de diferentes empresas ao longo do tempo. Os resultados indiciam que as posições em aberto podem ajudar a prever variações futuras dos prémios de CDS e retornos acionistas. Em acréscimo, verifica-se um aumento estatisticamente significativo das posições em aberto antes da divulgação de surpresas negativas nos resultados das empresas. O terceiro estudo mede os efeitos da proibição de posições longas em CDS sobre entidades soberanas pertencentes ao Espaço Único Europeu sem a detenção do ativo subjacente pelo comprador. A análise mostra um efeito negativo da proibição sobre a qualidade do mercado, pese embora se tenha assistido em simultâneo à redução da volatilidade. Por fim, são analisados os determinantes dos montantes associados a posições em aberto, com o intuito de compreender como o mercado de CDS pode influenciar o risco sistémico. Os resultados indicam que a assimetria de informação e a divergência de opiniões dos investidores influenciam aqueles montantes. Todavia, fatores sistemáticos como risco de contraparte, aversão ao risco e risco de re-financiamento parecem ser ainda mais relevantes por via do efeito que exercem no risco do balanço dos intermediários financeiros

Modelling, forecasting and riding credit risk in the Sterling Eurobond market

This thesis aims to make a contribution to the understanding of credit risk dynamics in the Sterling Eurobond market. The background to the thesis is the increasing size, complexity and volatility of all debt markets, where the tasks of measuring, understanding and forecasting credit risk are of central importance to investing institutions and to corporate and sovereign borrowers. We investigate the changes in the perceived credit quality of bond issuers through three different approaches. First, we describe the evolution of credit spreads over time, exploring whether they reflect economic fundamental, or whether they represent self-generated force. This question is central to the fixed income literature in general, and to the pricing of risky debt and credit derivatives in particular. The time-series properties of our credit spreads provide strong evidence of mean-reversion, non-linearities, and directional and persistentv olatility. All these stylised facts are captured by time-varying volatility models. Second, we assess the information value of bond ratings, by examining the dynamics of bond spreads around rating revision dates. In contrast to standard event studies we apply a novel GARCH model to the panel data. This lets us examine the effects of the regrading event on the volatility of bond yields as well as the yields themselves. We find that downgrades are viewed as informational events, but upgrades are not. An asymmetric pattern is also observed in the dynamics of volatility. Third, we build a predictive structural model for the downgrade probability using a two-step estimation procedure. This allows us to disentangle the effects of credit rating and various financial and accounting ratios. We find evidence of non-linear effects from both company indebtedness and credit risk. The forecasting model is benchmarked against both a naive model, and a more sophisticated neural network model. Unlike the field of default prediction, little research has been done on forecasting the downgrade event. Filling this gap is of interest to banks and investors in periods of relative economic stability, in the context of value-at-risk models, and for the pricing of credit risky instruments

Essays on credit risk, risk adjusted performance and economic capital in financial institutions

This dissertation consists of three autonomous essays, discussing the following topics: 1. the pricing of defaultable bonds, loans and plain vanilla credit derivatives, 2. the use of risk-adjusted performance measurement, for optimal portfolio management in the banking, asset management and insurance industries 3. return on economic capital as a measure of value created by the holding of bank assets and the operation of bank business units

Scaling up climate finance in the context of Covid-19: A science-based call for financial decision-makers

The sooner we act, the lower the risks of climate change and the higher the synergies between climate action and other societal benefits. That is a clear conclusion from the IPCC Special Report on the impacts of global warming of 1.5°C above pre-industrial levels. Financing a rapid transition to achieve the Paris Agreement goals requires significantly more investment and investment in a different set of low emission, climate resilient assets. The Covid-19 crisis increases the imperative to scale up climate action before these goals are out of reach. In particular, it is critical to increase the ability of developing countries to realize their climate ambitions in the context of the pandemic without increasing their debt burden.This new report, Scaling up climate finance in the context of Covid-19, aims to help financial decision-makers to align finance with sustainable development, accelerating the transition to a net-zero, climate resilient economy, based on the latest scientific findings and policy developments. It proposes four sets of actions to support developing countries in achieving this transition.This report aims to help financial decision-makers to align finance with sustainable development, accelerating the transition to a net-zero, climate resilient economy, based on the latest scientific findings and policy developments. It proposes four interventions to achieve this objective in the context of Covid-19

Fiancial Innovation, Structuring and Risk Transfer

These lecture notes are about financial innovations. We ask why are there some innovation and how is an innovative idea realized. This forces us to consider practical and structural aspects (regulations, taxation, markets) as key drivers of innovations and also basic formal aspects in valuation. Contents: Overview: Taxes and Regulation, Technology, Who Innovates, Life Cycle, Pricing and Hedging Discount Factors and No Arbitrage Investment: Rule Bases, Alpha, Beta, View and Trade, Fund Industry, Portfolio Theory Swaps and Financial Markets: IRS, TRS, ALM, ISDA Retail Structured Products Real Estate Asset Class, Green Banking, Demographic Risk Financial Crisis: Overview Leverage, Systemic Risk, Securitization, Pricin

Poor choices: the limits of competitive markets in the provision of essential services to low-income consumers

A major study of the problems faced by the poor in the market for seven essential services in the UK - energy, food, housing, water, telecoms, transport, and financial services. Together these represent 60% of spending by the poorest 30% of households

Market and Counterparty Credit Risk: Selected Computational and Managerial Aspects

The thesis can be placed within the literature on market and counterparty credit risk, contributing along the following three dimensions: 1. Interest rate risk (IRR) management: The thesis starts with an overview on asset liability management (ALM) in general and IRR management in particular. It then gives a novel procedure for structuring swap overlays for pensions funds, allowing for optimal hedging of IRR without affecting the strategic asset allocation (SAA). The thesis also offers an extension of the analysis of the Cairns (2004) stochastic interest rate model Deriving respective model-based sensitivity measures (Cairns deltas). It finally applies the model to a practical application, analyzing it when it comes to long-term contracts. 2. Pricing and managing counterparty credit risk A compact overview on counterparty credit risk (CCR) and credit valuation adjustment (CVA) is given. This is followed by a unique analyses around valuation, relevant accounting and regulatory requirements as well as pricing and mitigation, esp. Illustration of how CVA capital charge shows the tautology behind the discussions around regulatory requirements. The thesis contributes also to the discourse on debt valuation adjustment (DVA), e.g. showing that some aspects are not that unintuitive as presumed (e.g. DVA is being priced). 3. CVA modeling and wrong way risk. The thesis gives an overview on credit risk modeling in general and credit spreads in particular. It especially revisits the CVA for CDS model introduced by Brigo and Capponi (2010), giving e.g. A) a step-by-step implementation guide, esp. w.r.t to parts Brigo and Capponi (2010) left open; B) a computational tune-up, incl. a demonstration of its robustness across a variety of scenarios, and a realistic case study; C) a novel analysis of the Brigo & Capponi (2010) model in particular and CVA modeling in genera

Fiancial Innovation, Structuring and Risk Transfer

These lecture notes are about financial innovations. We ask why are there some innovation and how is an innovative idea realized. This forces us to consider practical and structural aspects (regulations, taxation, markets) as key drivers of innovations and also basic formal aspects in valuation. Contents: Overview: Taxes and Regulation, Technology, Who Innovates, Life Cycle, Pricing and Hedging Discount Factors and No Arbitrage Investment: Rule Bases, Alpha, Beta, View and Trade, Fund Industry, Portfolio Theory Swaps and Financial Markets: IRS, TRS, ALM, ISDA Retail Structured Products Real Estate Asset Class, Green Banking, Demographic Risk Financial Crisis: Overview Leverage, Systemic Risk, Securitization, Pricin