The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Mathematics of Quantitative Finance

The workshop on Mathematics of Quantitative Finance, organised at the Mathematisches Forschungsinstitut Oberwolfach from 26 February to 4 March 2017, focused on cutting edge areas of mathematical finance, with an emphasis on the applicability of the new techniques and models presented by the participants

Numerical methods to price interest rate derivatives based on LIBOR market model for forward rates

[Resumen] Los modelos de evolución de los tipos de interés son necesarios para valorar productos derivados de tipos y dependen de parámetros o funciones que se ajustan en base a ciertos productos que cotizan en mercado. En 1997, Brace, Gatarek y Musiela introducen el Libor Market Model (LMM) para los tipos forward de LIBOR. La ventaja de este modelo frente a los más clásicos es la observabilidad de los tipos forward en mercado y la calibración con productos que cotizan. En esta tesis se han planteado modelos de ecuaciones en derivadas parciales dentro del marco del LMM para valorar determinados productos derivados de tipos de interés, cuyos subyacentes son los tipos forward de LIBOR. En concreto, se valoraron contratos de tipo ratchet cap y rate based spread options. Una vez propuestos los modelos que rigen los precios de dichos productos financieros, se estudió la unicidad, existencia y regularidad de solución de los mismos así como algunas propiedades cualitativas. Para su resolución se utilizaron diversos métodos numéricos. En particular, el método de características Crank-Nicolson Lagrange Galerkin, técnicas de Monte Carlo y se obtuvo una expresión semianalítica utilizando soluciones fundamentales. Por último, se realizaron distintos tests académicos para chequear los métodos numéricos así como ejemplos de valoración de productos derivados cuyos datos eran tomados del mercado. Además, se realizó una comparativa de los tiempos de computación para todos los métodos numéricos considerados. En la última parte de la tesis, se propuso un modelo matemático para valorar contratos de tipo stock loan y se realizó el correspondiente análisis numérico. La valoración de un producto de este tipo implica resolver un problema de frontera libre y por tanto, no se engloba en la teoría clásica para ecuaciones de derivadas parciales que se utilizaba en la primera parte de la tesis. Se demostró la existencia y unicidad de solución así como la regularidad óptima de la solución en el espacio de las funciones con crecimiento polinomial. El método numérico empleado para valorar stock loans es el método de elementos finitos mediante el cual se reprodujeron ejemplos de valoración con datos reales, obteniendo buenos resultados y recuperando propiedades cualitativas demostradas teóricamente en la literatura

Essays on Basket Options Hedging and Irreversible Investment Valuation

Basket options are one of well-known newly-generated exotic options. As its name implies, it is an option on a portfolio of several assets. As the underlying basket offers more diversification, basket options gain increasing popularity in world financial markets as a fundamental instrument to manage portfolio risks. Examples thereof are equity index options which are traded on the exchange and usually contingent on at least 15 stocks, as well as currency basket options traded over the counter and written on over two currencies. Obviously, the unique feature of basket options is the basket underlying and a complex correlation structure therefore involved. It provides investors a couple of benefits like high diversification, a lower price against a portfolio of single options and so on, and meanwhile complicates the evaluation of basket options. The inherent challenge in pricing and hedging basket options stems primarily from the analytical intractability of the distribution of the basket. Moreover, the correlation between underlying assets is observed to be volatile over time. Due to the lack of standardized basket options traded in the market, the correlation structure can be only estimated from historical time series or from scarce option data. This further prevents us from exactly pricing basket options, and more importantly, perfectly hedging basket options. As a result, a partial- or super-hedge is often pursued in the literature when hedging basket options. Apart from these difficulties, we address another difficulty resulted from a great number of underlying assets in the basket while hedging basket options. If following the standard hedging method, a hedging portfolio for basket options should be related to all underlying assets in the basket. Clearly, if the number of the underlying assets is over 15, such a dynamic hedging strategy would be not only hardly implementable in many practical situations but also create a large transaction cost. In this sense, a static or buy-and-hold hedge strategy has its advantage in cost saving and hence hedge performance. As a result, the first part of this dissertation aims to design a static hedging strategy for European-style basket options and to analyze its hedging result. The newly developed static hedging strategies consist of traded plain-vanilla options on only subset of underlying assets. The optimal hedge is either super-- or partial-replicating, depending on the objective function taken in the numerical optimization. Considering the numerical challenge in the optimization with constraints on the initial capital (or some other hedging requirements) and the maximal number of hedging assets, hedging portfolios are suggested in this thesis to be obtained in two steps, namely pre-selection of the sub-hedge-basket and determination of optimal hedging instruments, more precisely, the optimal strikes of available plain-vanilla options on the chosen subset of the basket. Especially, a multivariate statistical technique, Principal Components Analysis, is introduced to identify dominant assets in the basket by taking into account all the coefficients that greatly influence the basket value, such as weight, volatility and correlation. As demonstrated by numerical examples, such hedging portfolios work satisfactorily, generating a reasonably small hedging error though by using only several assets. Real options are defined in the literature as to describe opportunities of investment in non-financial assets with some degree of freedom in decision making against the underlying uncertainty. As many other researchers, we are also interested in this topic and are going to study irreversible investment valuation in the second part of this dissertation. An extensive literature investigates the irreversible investment problem under uncertainty Despite a high reputation in academics, the real options theory is not widely adopted by corporate managers and practitioners due to the lack of transparency and simplicity of the standard real options approaches, i.e., the contingent claim analysis and the dynamic programming method. The second part of this dissertation first develops a Shadow Net Present Value rule by using a new approach in the real options theory. The method starts with identifying the expected present value from the investment and comes to the final conclusion via representing the expected present revenue in terms of the expected present value of the running supremum of the shadow revenue of the investment. By aiming at the net profit of the investment which is the mere concern of investors, this approach thus facilitates an intuitive understanding of the real options theory and also a wider application into the practice. Meanwhile, it generalizes the elegant explicit characterization of the investment decision rule to all exponential Levy processes: The optimal investment policy is a trigger strategy such that the investment is initiated at the first time when the value of the investment project comes to a critical threshold. As two extensions, this technique is then applied to two more complicated and practical models taking into consideration gradual capacity generation and risk neutrality, respectively. In each model, both qualitative and quantitative analysis is given on the investment feature and its relationship with related parameters.</p

Numerical Methods for Nonlinear Equations in Option Pricing

This thesis explores numerical methods for solving nonlinear partial differential equations (PDEs) that arise in option pricing problems. The goal is to develop or identify robust and efficient techniques that converge to the financially relevant solution for both one and two factor problems. To illustrate the underlying concepts, two nonlinear models are examined in detail: uncertain volatility and passport options. For any nonlinear model, implicit timestepping techniques lead to a set of discrete nonlinear equations which must be solved at each timestep. Several iterative methods for solving these equations are tested. In the cases of uncertain volatility and passport options, it is shown that the frozen coefficient method outperforms two different Newton-type methods. Further, it is proven that the frozen coefficient method is guaranteed to converge for a wide class of one factor problems. A major issue when solving nonlinear PDEs is the possibility of multiple solutions. In a financial context, convergence to the viscosity solution is desired. Conditions under which the one factor uncertain volatility equations are guaranteed to converge to the viscosity solution are derived. Unfortunately, the techniques used do not apply to passport options, primarily because a positive coefficient discretization is shown to not always be achievable. For both uncertain volatility and passport options, much work has already been done for one factor problems. In this thesis, extensions are made for two factor problems. The importance of treating derivative estimates consistently between the discretization and an optimization procedure is discussed. For option pricing problems in general, non-smooth data can cause convergence difficulties for classical timestepping techniques. In particular, quadratic convergence may not be achieved. Techniques for restoring quadratic convergence for linear problems are examined. Via numerical examples, these techniques are also shown to improve the stability of the nonlinear uncertain volatility and passport option problems. Finally, two applications are briefly explored. The first application involves static hedging to reduce the bid-ask spread implied by uncertain volatility pricing. While static hedging has been carried out previously for one factor models, examples for two factor models are provided. The second application uses passport option theory to examine trader compensation strategies. By changing the payoff, it is shown how the expected distribution of trading account balances can be modified to reflect trader or bank preferences

Modelling of and empirical studies on portfolio choice, option pricing, and credit risk

This thesis develops and applies a statistical spanning test for mean-coherent regular risk portfolios. Similarly in spirt to Huberman and Kandel (1987), this test can be implemented by means of a simple semi-parametric instrumental variable regression, where instruments have a direct link with a stochastic discount factor. Applications to different asset classes are studied. The results are compared to the conventional mean-variance approach. The second part of the thesis concerns option pricing under stochastic volatility and credit risk modelling. It is shown that modelling dynamics of the implied prices of volatility risk can improve out-of-sample option pricing performance. Finally, an equity-based structural model of credit risk with a constant elasticity of volatility assumption is discussed. This model might be particularly suitable for analysis of high yield fixed income instruments, where correlation between credit spreads and equity returns is substantial.

On two-sided controls of a linear diffusion

siirretty Doriast

Bitcoin : users’ characteristics, motivations and investment behaviours

In less than a decade, the cryptocurrency known as Bitcoin has gone from a fringe phenomenon to a topic of increasing interest to academia and mainstream investors. However, despite the growing body of research seeking to understand Bitcoin, the pseudonymous, decentralised, and globally-diffused nature of its user base means that the individuals who use it remain poorly understood. In particular, the motivations, risk-appreciation, and investment behaviours of early adopters and innovators are subject to supposition in the absence of data derived from the user base. This thesis seeks to address this gap in knowledge by employing a multi-stage, mixed methodology approach and a theoretical framework to understand the Bitcoin user base. Utilising semantic analysis, a survey of online cryptocurrency communities, and econometric time-series analysis, this thesis addresses the extent and nature of Bitcoin in hedging; how individual users perceive their own motivations, uses, and risks that have driven their behaviour; and the nature of the relationship between the prices of cryptocurrency and indices of confidence. Analysis of the data determined that the use of Bitcoin as an instrument of hedging is limited, and influenced by political and institutional factors. Likewise, its motivations, uses, and risks are reflective of the users’ political ideology, with the community and marketplace becoming more sophisticated as they evolve over time. Additionally, despite several case studies demonstrating risk-averse adoption of Bitcoin, there is no relationship between its prices and confidence.Doctor of Philosoph

Innovation in a Circular Economy: Conceptual, empirical and policy underpinnings for transition through an eco-innovation pathway

As the world seeks answers to the defining challenges of climate change and environmental sustainability, several hypotheses are being canvased in the search for a solution to decouple economic growth and social development from resource exploitation. Among those, the circular economy (CE) emerged as an operational response defined by its opposition to a harvesting-wasting economic model, proposing instead restorative and regenerative activities. But reconfiguring existing paradigms is not trivial. Aligning innovation activities with more sustainable paths is a central requirement for the desired socio-techno-economic paradigm shift. This work proposes that a new pathway is needed for gearing the sustainable innovation agenda towards a CE, and foster structural change. CE-inducing eco-innovation (EI) must, however, be monitored and measured, and implications to socio-cultural agents, organisational strategies and policy priorities have to be bore in mind, if we are to ascertain if progress is being made. As CE and the EI – CE nexus research is still in its early days, this work adds to the discussion by contributing (1) to the theoretical development of these concepts and their interrelations; (2) to the empirical definition of pro CE EI proxies; and (3) to the prospective anticipation of CE developments. Within the sustainability debate, and using an innovation studies perspective, this research adopted a mixed methods approach, using both quantitative and qualitative methods such as literature reviews, bibliometrics, patent and trademark analysis (using the specific case of Portugal), and foresight techniques (Delphi study). The overall findings suggest that CE’s main ideas are arguably timely. CE’s establishment within the sustainability debate seems, nevertheless, dependent on overcoming short term barriers constraining its further development, of technological and economic nature, but also of a socio-cultural kind. CE is argued as a multidimensional, multi-actor approach reliant on “systemic transformative” innovation, thus dependent on a combination of “harder”, (technological, R&D-driven), and “softer” (non-technological change in social and business culture) knowledge. The empirical diagnosis of an innovation system’s pro circularity tendencies proved to be informative as to assess convergence to circularity. In the Portuguese case, it successfully shed light on ongoing dynamics related with signs of effective transformation towards CE activities, even if highlighting structural limitations associated with systemic failures regarding actors and networks. Redirecting innovation systems towards a more “circular” paradigm is, therefore, deeply dependent on an institutional “coordination role” enabling “framework conditions” directly linked to a systemic action. That is, associating bottom-up measures to top-down policies in a coherent strategic roadmap, in order to avoid mismatches and contradictory incentives. This pointed to the usefulness of rethinking innovation policy design. In one hand, to address market and system failures, leading to underinvestment and lack of connectivity in innovation. In the other hand, to promote the diffusion of CE related information for enterprises and civil society, in order to encourage market awareness and change mind-sets towards “circular” behaviours. As the conceptual and practical implementation challenge remains pressing, this work added important underpinnings for fine-tuning a CE inducing “policy mix”.Num mundo crescentemente interdependente, as alterações climáticas e a sustentabilidade ambiental são questões globais complexas. A importância de dissociar desenvolvimento da exploração de recursos tem propiciado um alargamento de horizontes a novos conceitos. Nesse contexto, a economia circular emergiu como uma resposta operacional, definida pela sua oposição ao modelo económico atual de exploração/desperdício. Contrapõe, ao invés, processos restaurativos e regenerativos. A reconfiguração dos paradigmas existentes, a este nível, não é, contudo, algo trivial. Uma vez que o alinhamento das atividades de inovação com objetivos mais sustentáveis é um requisito central na alteração de paradigma sócio-tecno-económico, este trabalho foca a necessidade de orientar a agenda de inovação para a “circularidade”. A eco-inovação pro-circularidade deve, no entanto, ser monitorizada e medida, e as implicações para os agentes socioculturais, estratégias organizacionais e prioridades políticas levadas em conta, se quisermos verificar o seu progresso. Nesse âmbito, pretendeu-se contribuir para o debate em curso contribuindo para: 1) uma melhor compreensão teórica do papel da eco-inovação na implementação de uma economia circular; 2) a definição e teste de proxies empíricas de inovação pro-circularidade; 3) o desenvolvimento de uma visão prospetiva de futuros desenvolvimentos nesta área. No contexto do debate da sustentabilidade, e usando uma perspetiva baseada nos estudos da inovação, foram adotados métodos quantitativos e qualitativos, incluindo revisões de literatura, métodos bibliométricos, análise de patentes e de marcas comerciais (usando o caso específico de Portugal), assim como o uso do método prospetivo Delphi. As conclusões gerais sugerem que as principais ideias da economia circular são indiscutivelmente oportunas. Dentro do debate da sustentabilidade o estabelecimento de uma economia circular parece, no entanto, dependente de se vencerem barreiras de curto prazo, de natureza tecnológica, económica e sociocultural. A abordagem preconizada pela economia circular é assim tida como multidimensional, multi-ator, dependente de uma inovação sistémica "transformadora”, compreendendo não só inovação tecnológica, mas também mudanças institucionais abrangentes quanto a políticas públicas, mercados e práticas sociais. O diagnóstico empírico das tendências pró-circularidade de um sistema de inovação provou ser informativo nessa avaliação. No caso português, permitiu conhecer as atuais dinâmicas, sublinhando sinais de transformação efetivas em direção a atividades circulares, ao mesmo tempo que assinalou as limitações estruturais associadas a falhas sistémicas quanto aos atores e redes (interconexões). Redirecionar os sistemas de inovação para um paradigma mais “circular” é, portanto, profundamente dependente de um “papel de coordenação” institucional que permita “condições de enquadramento” diretamente ligadas a uma ação sistémica. Isto é, associando medidas bottom-up e top-down num roteiro estratégico coerente, a fim de evitar desequilíbrios e incentivos contraditórios. Importa, por isso, repensar igualmente os instrumentos das políticas de inovação. Por um lado, resolvendo falhas de mercado e sistema, que levam a sub-investimento e falta de conectividade. Por outro, promovendo a difusão de informação para empresas e sociedade civil, a fim de estimular a conscientização e mudar mentalidades em relação a comportamentos “circulares”. O desafio de implementação continua a ser premente, este trabalho pretendeu contudo acrescentar ao debate tendo em vista contribuir para o ajuste do “mix de políticas” indutoras de circularidade

Mathematical methods for valuation and risk assessment of investment projects and real options

In this thesis, we study the problems of risk measurement, valuation and hedging of financial positions in incomplete markets when an insufficient number of assets are available for investment (real options). We work closely with three measures of risk: Worst-Case Scenario (WCS) (the supremum of expected values over a set of given probability measures), Value-at-Risk (VaR) and Average Value-at-Risk (AVaR), and analyse the problem of hedging derivative securities depending on a non-traded asset, defined in terms of the risk measures via their acceptance sets. The hedging problem associated to VaR is the problem of minimising the expected shortfall. For WCS, the hedging problem turns out to be a robust version of minimising the expected shortfall; and as AVaR can be seen as a particular case of WCS, its hedging problem is also related to the minimisation of expected shortfall. Under some sufficient conditions, we solve explicitly the minimal expected shortfall problem in a discrete-time setting of two assets driven by correlated binomial models. In the continuous-time case, we analyse the problem of measuring risk by WCS, VaR and AVaR on positions modelled as Markov diffusion processes and develop some results on transformations of Markov processes to apply to the risk measurement of derivative securities. In all cases, we characterise the risk of a position as the solution of a partial differential equation of second order with boundary conditions. In relation to the valuation and hedging of derivative securities, and in the search for explicit solutions, we analyse a variant of the robust version of the expected shortfall hedging problem. Instead of taking the loss function $l(x) = [x]^+$ we work with the strictly increasing, strictly convex function $L_{\epsilon}(x) = \epsilon \log \left( \frac{1+exp\{−x/\epsilon\} }{ exp\{−x/\epsilon\} } \right)$. Clearly $lim_{\epsilon \rightarrow 0} L_{\epsilon}(x) = l(x)$. The reformulation to the problem for L_{\epsilon}(x) also allow us to use directly the dual theory under robust preferences recently developed in [82]. Due to the fact that the function $L_{\epsilon}(x)$ is not separable in its variables, we are not able to solve explicitly, but instead, we use a power series approximation in the dual variables. It turns out that the approximated solution corresponds to the robust version of a utility maximisation problem with exponential preferences $(U(x) = −\frac{1}{\gamma}e^{-\gamma x})$ for a preferenes parameter $\gamma = 1/\epsilon$. For the approximated problem, we analyse the cases with and without random endowment, and obtain an expression for the utility indifference bid price of a derivative security which depends only on the non-traded asset