Mathematical Models for Interest Rate Dynamics

We present a study of mathematical models of interest rate products. After an introduction to the mathematical framework, we study several basic one-factor models, and then explore multifactor models. We also discuss the Heath-Jarrow- Morton model and the LIBOR Market model. We conclude with a discussion of some modified models that involve stochastic volatility

A selective overview of nonparametric methods in financial econometrics

This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and time-dependent diffusion processes, and estimation of transition densities and state price densities. We first briefly describe the problems and then outline main techniques and main results. Some useful probabilistic aspects of diffusion processes are also briefly summarized to facilitate our presentation and applications.Comment: 32 pages include 7 figure

A New Proposal for Collection and Generation of Information on Financial Institutions' Risk: the case of derivatives

This article aims at providing a new alternative for the collection of information on risks taken by financial institutions, which enables the calculation of risk tools usually used in risk management, such as VaR and stress tests. This approach should help risk managers, off-site supervision and academics in assessing the potential risks in financial institutions principally due to derivatives positions. The basic idea, for linear financial instruments, like the traditionally used by the management risk systems, is to reduce positions in risk factors and then mapping by vertices. For the nonlinear financial instruments all of the positions in different types of options – European, Americans, exotic, etc.– are represented as plain vanilla European options or replicated by portfolios of plain vanilla European options. The methodology was applied to Brazil, within the worst scenarios during the period from 1994 to 2004, and the paper demonstrates that the proposed approach captured the risks satisfactorily in the analyzed portfolios, including the risk existent in the strategies involving options, given an accepted error margin. This approach could be useful for regulators, risk managers; financial institutions and risk management modeling as it can be used as an input in general risk management models.

An asset and liability management model incorporating uncertainty

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Asset and Liability Management (ALIvI) is a well-established method, which enables companies to match future liabilities with future cash flow streams of assets. The first stage is to develop a deterministic model with forecast cash flow streams. In reality this can lead to results that are often volatile to deviations of future cash flows from their predicted values. There are two main stages to this problem. Firstly, there is the issue of representing the future uncertainties. To this end we have developed a scenario generator that forecasts alternative realizations of future cash flows streams of different assets using alternative scenarios about a financial Index and the Capital Asset Pricing Model (CAPM). Considering this with the deterministic model leads to the creation of ALM models which incorporate uncertainty. Having represented the uncertainty, we use an optimisation model to generate the current decisions concerning acquisition and disposal of assets. This model is a two stage stochastic programming model that aims to achieve targeted cash flows for each future year. Risk is represented in the form of assigning shares to different risk groups. In this thesis we describe our models of randomness and how they are captured in the two-stage stochastic programming model. We compare our model to a mean-variance representation. Both models are simulated through time. Backtesting is used to investigate the quality of both approaches

Combining Hodrick-Prescott Filtering with a Production Function Approach to Estimate Output Gap

Many models were used to identify the factors affecting the demand for overnight funds by commercial banks. Theses models overcome overdispersion problems caused by excess of zeros found in the dataset. Generalized Linear Latent and Mixed Models (GLLAMM) constitute a class of models which allows the identification of both the direct and indirect effects of rediscount rate through the inclusion of random effects in the intercept (incorporating specific effects for each bank) and other coefficients (identifying individual behavior of each bank regarding the same stimuli). The results suggest the use of overnight funds is mainly influenced by the opening amount in bank reserves, by the net value of operations in the SELIC clearinghouse, by the rediscount rate, by the volatility of in bank reserves and by the reserve requirements on demand deposits.The proposed methodology combines two of the most important techniques to estimate output gap: the production function approach and the Hodrick-Prescott .ltering. Three main advantages can be derived from this method: (i) it adds some economic structure to a .filtering method, (ii) it can be easily adapted to incorporate new characteristics into the filter and (iii) it simultaneously produces estimates for potential output and its unobservable components.