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.

``String'' formulation of the Dynamics of the Forward Interest Rate Curve

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial (possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation of the standard European option problem). We also show how the ``string'' formulation simplifies into a standard N-factor model under a Galerkin approximation.Comment: 24 pages, European Physical Journal B (in press

Stochastic volatility

Given the importance of return volatility on a number of practical financial management decisions, the efforts to provide good real- time estimates and forecasts of current and future volatility have been extensive. The main framework used in this context involves stochastic volatility models. In a broad sense, this model class includes GARCH, but we focus on a narrower set of specifications in which volatility follows its own random process, as is common in models originating within financial economics. The distinguishing feature of these specifications is that volatility, being inherently unobservable and subject to independent random shocks, is not measurable with respect to observable information. In what follows, we refer to these models as genuine stochastic volatility models. Much modern asset pricing theory is built on continuous- time models. The natural concept of volatility within this setting is that of genuine stochastic volatility. For example, stochastic-volatility (jump-) diffusions have provided a useful tool for a wide range of applications, including the pricing of options and other derivatives, the modeling of the term structure of risk-free interest rates, and the pricing of foreign currencies and defaultable bonds. The increased use of intraday transaction data for construction of so-called realized volatility measures provides additional impetus for considering genuine stochastic volatility models. As we demonstrate below, the realized volatility approach is closely associated with the continuous-time stochastic volatility framework of financial economics. There are some unique challenges in dealing with genuine stochastic volatility models. For example, volatility is truly latent and this feature complicates estimation and inference. Further, the presence of an additional state variable - volatility - renders the model less tractable from an analytic perspective. We examine how such challenges have been addressed through development of new estimation methods and imposition of model restrictions allowing for closed-form solutions while remaining consistent with the dominant empirical features of the data.Stochastic analysis

Pricing and hedging bond options and sinking-fund bonds under the CIR model

This article derives simple closed-form solutions for computing Greeks of zero-coupon and coupon-bearing bond options under the CIR interest rate model, which are shown to be accurate, easy to implement, and computationally highly e cient. These novel analytical solutions allow us to extend the literature in two other directions. First, the static hedging portfolio approach is used for pricing and hedging American-style plain-vanilla zero-coupon bond options under the CIR model. Second, we derive analytically the comparative static properties of sinking-fund bonds under the same interest rate modeling setup.Manuela Larguinho and Carlos A. Braumann belong to the research center CIMA (Centro de Investigação em Matemática e Aplicações, Instituto de Investigação e Formação Avançada, Universidade de Évora), supported by FCT (Fundação para a Ciência e a Tecnologia, Portugal), project UID/04674/2020. José Carlos Dias belongs to the Business Research Unit (BRU-IUL) and acknowledges the support provided by FCT [grant number UIDB/00315/2020]

Credit Modelling: Generating Spread Dynamics with Intensities and Creating Dependence with Copulas

The thesis is an investigation into the pricing of credit risk under the intensity framework with a copula generating default dependence between obligors. The challenge of quantifying credit risk and the derivatives that are associated with the asset class has seen an explosion of mathematical research into the topic. As credit markets developed the modelling of credit risk on a portfolio level, under the intensity framework, was unsatisfactory in that either: 1. The state variables of the intensities were driven by diffusion processes and so could not generate the observed level of default correlation (see Schönbucher (2003a)) or, 2. When a jump component was added to the state variables, it solved the problem of low default correlation, but the model became intractable with a high number of parameters to calibrate to (see Chapovsky and Tevaras (2006)) or, 3. Use was made of the conditional independence framework (see Duffie and Garleanu (2001)). Here, conditional on a common factor, obligors’ intensities are independent. However the framework does not produce the observed level of default correlation, especially for portfolios with obligors that are dispersed in terms of credit quality. Practitioners seeking to have interpretable parameters, tractability and to reproduce observed default correlations shifted away from generating default dependence with intensities and applied copula technology to credit portfolio pricing. The one factor Gaussian copula and some natural extensions, all falling under the factor framework, became standard approaches. The factor framework is an efficient means of generating dependence between obligors. The problem with the factor framework is that it does not give a representation to the dynamics of credit risk, which arise because credit spreads evolve with time. A comprehensive framework which seeks to address these issues is developed in the thesis. The framework has four stages: 1. Choose an intensity model and calibrate the initial term structure. 2. Calibrate the variance parameter of the chosen state variable of the intensity model. 3. When extended to a portfolio of obligors choose a copula and calibrate to standard market portfolio products. 4. Combine the two modelling frameworks, copula and intensity, to produce a dynamic model that generates dependence amongst obligors. The thesis contributes to the literature in the following way: • It finds explicit analytical formula for the pricing of credit default swaptions with an intensity process that is driven by the extended Vasicek model. From this an efficient calibration routine is developed. Many works (Jamshidian (2002), Morini and Brigo (2007) and Schönbucher (2003b)) have focused on modelling credit swap spreads directly with modified versions of the Black and Scholes option formula. The drawback of using a modified Black and Scholes approach is that pricing of more exotic structures whose value depend on the term structure of credit spreads is not feasible. In addition, directly modelling credit spreads, which is required under these approaches, offers no explicit way of simulating default times. In contrast, with intensity models, there is a direct mechanism to simulate default times and a representation of the term structure of credit spreads is given. Brigo and Alfonsi (2005) and Bielecki et al. (2008) also consider intensity modelling for the purposes of pricing credit default swaptions. In their works the dynamics of the intensity process is driven by the Cox Ingersoll and Ross (CIR) model. Both works are constrained because the parameters of the CIR model they consider are constant. This means that when there is more than one tradeable credit default swaption exact calibration of the model is usually not possible. This restriction is not in place in our methodology. • The thesis develops a new method, called the loss algorithm, in order to construct the loss distribution of a portfolio of obligors. The current standard approach developed by Turc et al. (2004) requires differentiation of an interpolated curve (see Hagan and West (2006) for the difficulties of such an approach) and assumes the existence of a base correlation curve. The loss algorithm does not require the existence of a base correlation curve or differentiation of an interpolated curve to imply the portfolio loss distribution. • Schubert and Schönbucher (2001) show theoretically how to combine copula models and stochastic intensity models. In the thesis the Schubert and Schönbucher (2001)framework is implemented by combining the extended Vasicek model and the Gaussian copula model. An analysis of the impact of the parameters of the combined models and how they interact is given. This is as follows: – The analysis is performed by considering two products, securitised loans with embedded triggers and leverage credit linked notes with recourse. The two products both have dependence on two obligors, a counterparty and a reference obligor. – Default correlation is shown to impact significantly on pricing. – We establish that having large volatilities in the spread dynamics of the reference obligor or counterparty creates a de-correlating impact: the higher the volatility the lower the impact of default correlation. – The analysis is new because, classically, spread dynamics are not considered when modelling dependence between obligors. • The thesis introduces a notion called the stochastic liquidity threshold which illustrates a new way to induce intensity dynamics into the factor framework. • Finally the thesis shows that the valuation results for single obligor credit default swaptions can be extended to portfolio index swaptions after assuming losses on the portfolio occur on a discretised set and independently to the index spread level

Regulation of New Financial Instruments Under the Federal Securities and Commodities Laws

In the last few years, an endless stream of exotic financial instruments conjured by Wall Street wizards literally has taken the financial community by storm, fundamentally altering market trading practices and pitting institutions against each other in an intense competition for development of still more innovative instruments. These products--which include various types of swaps, options, forward contracts, and price guarantees--now are being offered to and traded by every major financial institution and multinational corporation in the world, as well as by governments and individuals, and nothing indicates that the unprecedented growth of the markets for such instruments is likely to sub-side any time soon. To the contrary, the trend clearly is toward increased product proliferation and the addition of still more arcane and complex trading vehicles to the already dizzying array now available. The speed with which these products have reached the markets plainly has outstripped the ability of accountants, lawyers,and regulators to keep pace with their development and to deter-mine their status under prevailing law and practices. In particular,although these products to some extent parallel existing instruments within the traditional regulatory jurisdiction of the Securities and Exchange Commission (SEC) and the Commodity Futures Trading Commission (CFTC), their new and varied features have created substantial uncertainty as to the proper locus of regulatory jurisdiction over their trading. Whether the SEC, CFTC, or other agencies have exclusive or concurrent jurisdiction with respect to these new instruments, or whether they even have jurisdiction at all, often is unclear. This Article first will discuss the general scope of the commodities and securities industries and the respective regulatory spheres of the CFTC and SEC. This background is essential to any under-standing of the nature and regulatory status of new financial instruments, many of which are derived from more traditional types of investment and trading vehicles within the jurisdiction of these agencies, and all of which have been structured to minimize the likelihood of being encompassed within such jurisdiction. Indeed,it is virtually impossible to appreciate the potential regulatory problems associated with the offer and sale of such instruments

Convertible bond underpricing in the french market : an empirical study

The pricing of convertible bonds is a fairly unstudied field of asset pricing due to the instruments’ complex nature and its niche character. The aim of this dissertation is to compute model implied prices for convertible bonds and compare it to their market value in order to determine whether the market truly underprices convertible bonds, a financial theory that has been discussed broadly in the academic community. As a pricing model I applied a Monte Carlo simulation for stock prices and determined the optimal exercise strategy through the Least-Squares method. With this methodology I priced 34 convertible bonds in the French market and obtained an average underpricing of 4.17%, which reduces to 2.72% when excluding outliers. The results align with previous conducted studies of the French market but are in contrast with some other empirical results in the United States, but due to the substantial difference in convertible bond markets worldwide a direct comparison is not appropriate. Although the finding supports the general claim of convertible bond underpricing and encourages investors to engage in hedging strategies, the lack of substantial research in the European market calls for further empirical studies and improvements of the work presented.A valorização de obrigações convertíveis é um campo muito pouco estudado da valorização de ativos devido à complexidade dos instrumentos e ao seu carácter de nicho. O objetivo desta dissertação é calcular os preços implícitos de obrigações convertíveis e compará-los com o seu valor de mercado a fim de determinar se o seu mercado está realmente subvalorizado, um fenómeno frequentemente descrito por outros autores. Como modelo de preços, apliquei uma simulação Monte-Carlo para os preços das ações e determinei a estratégia ótima de exercício através do método de Least-Squares. Com esta metodologia, fixei o preço de 34 obrigações convertíveis no mercado francês e obtive uma subvalorização média de 4,17%, que reduz para 2,72% ao excluir os outliers. Os resultados estão em linha com estudos anteriores realizados no mercado francês, mas contrastam com outros resultados empíricos nos Estados Unidos; no entanto, devido à diferença substancial nos mercados de obrigações convertíveis em todo o mundo, uma comparação direta não é apropriada. Embora a conclusão apoie a alegação geral de subvalorização de obrigações convertíveis e encoraje os investidores a adotar estratégias de cobertura, a falta de investigação substancial no mercado europeu requer mais estudos empíricos e melhorias do trabalho apresentado