Poisson-Guassian Processes and the Bond Markets

Poisson-Guassian Processes and the Bond Markets
Author: Sanjiv Ranjan Das
Publisher:
Total Pages: 34
Release: 2010
Genre:
ISBN:

That interest rates move in a discontinuous manner is no surprise to participants in the bond markets. This paper proposes and estimates a class of Poisson-Gaussian processes that allow for jumps in interest rates. Estimation is undertaken using exact continuous-time and discrete-time estimators. Analytical derivations of the characteristic functions, moments and density functions of jump-diffusion stochastic process are developed and employed in empirical estimation. These derivations are general enough to accommodate any jump distribution. We find that jump processes capture empirical features of the data which would not be captured by diffusion models. The models in the paper enable an assessment of the impact of Fed activity and day-of-week effects on the stochastic process for interest rates. There is strong evidence that existing diffusion models would be well-enhanced by jump processes.

Dynamic Asset Pricing Theory

Dynamic Asset Pricing Theory
Author: Darrell Duffie
Publisher: Princeton University Press
Total Pages: 488
Release: 2010-01-27
Genre: Business & Economics
ISBN: 1400829208

This is a thoroughly updated edition of Dynamic Asset Pricing Theory, the standard text for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis, so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. Readers will be particularly intrigued by this latest edition's most significant new feature: a chapter on corporate securities that offers alternative approaches to the valuation of corporate debt. Also, while much of the continuous-time portion of the theory is based on Brownian motion, this third edition introduces jumps--for example, those associated with Poisson arrivals--in order to accommodate surprise events such as bond defaults. Applications include term-structure models, derivative valuation, and hedging methods. Numerical methods covered include Monte Carlo simulation and finite-difference solutions for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. A system of appendixes reviews the necessary mathematical concepts. And references have been updated throughout. With this new edition, Dynamic Asset Pricing Theory remains at the head of the field.

Financial Risk and Derivatives

Financial Risk and Derivatives
Author: Henri Loubergé
Publisher: Springer Science & Business Media
Total Pages: 139
Release: 2012-12-06
Genre: Business & Economics
ISBN: 9400918267

Financial Risk and Derivatives provides an excellent illustration of the links that have developed in recent years between the theory of finance on one hand and insurance economics and actuarial science on the other. Advances in contingent claims analysis and developments in the academic and practical literature dealing with the management of financial risks reflect the close relationships between insurance and innovations in finance. The book represents an overview of the present state of the art in theoretical research dealing with financial issues of significance for insurance science. It will hopefully provide an impetus to further developments in applied insurance research.

An Efficient Generalized Discrete-time Approach to Poisson-Gaussian Bond Option Pricing in the Heath-Jarrow-Morton Model

An Efficient Generalized Discrete-time Approach to Poisson-Gaussian Bond Option Pricing in the Heath-Jarrow-Morton Model
Author: Sanjiv Ranjan Das
Publisher:
Total Pages: 60
Release: 1997
Genre: Bonds
ISBN:

Term structure models employing Poisson-Gaussian processes may be used to accommodate the observed skewness and kurtosis of interest rates. This paper extends the discrete-time, pure-Gaussian version of the Heath-Jarrow-Morton model to the pricing" of American-type bond options when the underlying term structure of interest rates follows a Poisson-Gaussian process. The Poisson-Gaussian process is specified using a hexanomial tree (six nodes emanating from each node), and the tree is shown to be recombining. The scheme is parsimonious and convergent. This model extends the class of HJM models by (i) introducing a more generalized volatility specification than has been used so far, and (ii) inducting jumps, yet retaining lattice recombination, thus making the model useful for practical applications

Financial Derivatives

Financial Derivatives
Author: Jamil Baz
Publisher: Cambridge University Press
Total Pages: 358
Release: 2004-01-12
Genre: Business & Economics
ISBN: 9780521815109

Publisher Description

Implementing Models in Quantitative Finance: Methods and Cases

Implementing Models in Quantitative Finance: Methods and Cases
Author: Gianluca Fusai
Publisher: Springer Science & Business Media
Total Pages: 606
Release: 2007-12-20
Genre: Business & Economics
ISBN: 3540499598

This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.

Mathematics of the Bond Market: A Lévy Processes Approach

Mathematics of the Bond Market: A Lévy Processes Approach
Author: Michał Barski
Publisher: Cambridge University Press
Total Pages: 401
Release: 2020-04-23
Genre: Business & Economics
ISBN: 1107101298

Analyses bond market models with Lévy stochastic factors, suitable for graduates and researchers in probability and mathematical finance.