Environment Cockpit

The Environment Cockpit was designed for the BNP Paribas eCommerce technical support team: just as pilots use a cockpit to control an aircraft, our Environment Cockpit is a tool to help visualize and control computing facilities. Specifically, it serves to centralize information from existing tools and to provide a user-friendly and dynamic graphical representation of different elements of the system to help diagnose alerts accurately and effectively. This project defined the scope of the tool, implemented a project prototype with WPF and Graph# library, designed a user interface model and constructed a prototype implementation

Construction of a zero-coupon yield curve for the Nairobi Securities Exchange and its application in pricing derivatives

Thesis submitted in partial fulfillment of the requirements for the degree for PhD in Financial Mathematics at Strathmore UniversityYield curves are used to forecast interest rates for different products when their risk parameters are known, to calibrate no-arbitrage term structure models, and (mostly by investors) to detect whether there is arbitrage opportunity. By yield curve information, investors have opportunity of immunizing/hedging their investment portfolios against financial risks if they have to make an investment with some determined time of maturity. Private sector firms look at yields of different maturities and then choose their borrowing strategy. The differences in yields for long maturity and short maturities are an important indicator for central bank to use in monetary policy process. These differences may show the tightness of the government monetary policy and can be monitored to predict recession in coming years. A lot of research has been done in yield curve modeling and as we will see later in the thesis, most of the models developed had one major shortcoming: non differentiability at the interpolating knot points. The aim of this thesis is to construct a zero coupon yield curve for Nairobi Securities Exchange, and use the risk- free rates to price derivatives, with particular attention given to pricing coffee futures. This study looks into the three methods of constructing yield curves: by use of spline-based models, by interpolation and by using parametric models. We suggest an improvement in the interpolation methods used in the most celebrated spline-based model, monotonicity-preserving interpolation on r(t). We also use operator form of numerical differentiation to estimate the forward rates at the knot points, at which points the spot curve is non-differential. In derivative pricing, dynamical processes (Ito^ processes) are reviewed; and geometric Brownian motion is included, together with its properties and applications. Conventional techniques used in estimation of the drift and volatility parameters such as historical techniques are reviewed and discussed. We also use the Hough Transform, an artificial intelligence method, to detect market patterns and estimate the drift and volatility parameters simultaneously. We look at different ways of calculating derivative prices. For option pricing, we use different methods but apply Bellalahs models in calculation of the Coffee Futures prices because they incorporate an incomplete information parameter

Stochastic and copula models for credit derivatives

We prove results relating to the exit time of a stochastic process from a region in N-dimensional space. We compute certain stochastic integrals involving the exit time. Taking a Gaussian copula model for the hitting time behavior, we prove several results on the sensitivity of quantities connected with the hitting times to parameters of the model, as well as the large-N behavior. We discuss the relationship of these results to certain credit derivative instruments. Relevant simulations are presented

Translating parameter estimation problems from EASY-FIT to SOCS

Mathematical models often involve unknown parameters that must be fit to experimental data. These so-called parameter estimation problems have many applications that may involve differential equations, optimization, and control theory. EASY-FIT and SOCS are two software packages that solve parameter estimation problems. In this thesis, we discuss the design and implementation of a source-to-source translator called EFtoSOCS used to translate EASY FIT input into SOCS input. This makes it possible to test SOCS on a large number of parameter estimation problems available in the EASY-FIT problem database that vary both in size and difficulty.Parameter estimation problems typically have many locally optimal solutions, and the solution obtained often depends critically on the initial guess for the solution. A 3-stage approach is followed to enhance the convergence of solutions in SOCS. The stages are designed to use an initial guess that is progressively closer to the optimal solution found by EASY-FIT. Using this approach we run EFtoSOCS on all translatable problems (691) from the EASY-FIT database. We find that all but 7 problems produce converged solutions in SOCS. We describe the reasons that SOCS was not able solve these problems, compare the solutions found by SOCS and EASY-FIT, and suggest possible improvements to both EFtoSOCS and SOCS

Quantitative Modeling of Credit Derivatives

The recent financial crisis has revealed major shortcomings in the existing approaches for modeling credit derivatives. This dissertation studies various issues related to the modeling of credit derivatives: hedging of portfolio credit derivatives, calibration of dynamic credit models, and modeling of credit default swap portfolios. In the first part, we compare the performance of various hedging strategies for index collateralized debt obligation (CDO) tranches during the recent financial crisis. Our empirical analysis shows evidence for market incompleteness: a large proportion of risk in the CDO tranches appears to be unhedgeable. We also show that, unlike what is commonly assumed, dynamic models do not necessarily perform better than static models, nor do high-dimensional bottom-up models perform better than simpler top-down models. On the other hand, model-free regression-based hedging appears to be surprisingly effective when compared to other hedging strategies. The second part is devoted to computational methods for constructing an arbitrage-free CDO pricing model compatible with observed CDO prices. This method makes use of an inversion formula for computing the aggregate default rate in a portfolio from expected tranche notionals, and a quadratic programming method for recovering expected tranche notionals from CDO spreads. Comparing this approach to other calibration methods, we find that model-dependent quantities such as the forward starting tranche spreads and jump-to-default ratios are quite sensitive to the calibration method used, even within the same model class. The last chapter of this dissertation focuses on statistical modeling of credit default swaps (CDSs). We undertake a systematic study of the univariate and multivariate properties of CDS spreads, using time series of the CDX Investment Grade index constituents from 2005 to 2009. We then propose a heavy-tailed multivariate time series model for CDS spreads that captures these properties. Our model can be used as a framework for measuring and managing the risk of CDS portfolios, and is shown to have better performance than the affine jump-diffusion or random walk models for predicting loss quantiles of various CDS portfolios