Exact Solutions for Bond and Option Prices with Systematic Jump Risk

Exact Solutions for Bond and Option Prices with Systematic Jump Risk

Author: Sanjiv Ranjan Das

Publisher:

Published: 2009

Total Pages:

ISBN-13:

DOWNLOAD EBOOK

A variety of realistic economic considerations make jump- diffusion models of interest rate dynamics an appealing modeling choice to price interest rate contingent claims. However, exact closed form solutions for bond prices when interest rates follow a mixed jump-diffusion process have proved very hard to derive. This paper puts forward two new models of interest rate dynamics which combine infrequent, discrete changes in the interest rate level, modeled as a jump process, with short lived, mean reverting shocks, modeled as a diffusion process. The two models differ in the way jumps affect the central tendency of interest rates; in one case shocks are temporary, in the other shocks are permanent. We derive exact closed form solutions for the price of a discount bond, and computationally tractable schemes to price bond options.


Option Pricing, Interest Rates and Risk Management

Option Pricing, Interest Rates and Risk Management

Author: Elyès Jouini

Publisher: Cambridge University Press

Published: 2001

Total Pages: 324

ISBN-13: 9780521792370

DOWNLOAD EBOOK

This 2001 handbook surveys the state of practice, method and understanding in the field of mathematical finance. Every chapter has been written by leading researchers and each starts by briefly surveying the existing results for a given topic, then discusses more recent results and, finally, points out open problems with an indication of what needs to be done in order to solve them. The primary audiences for the book are doctoral students, researchers and practitioners who already have some basic knowledge of mathematical finance. In sum, this is a comprehensive reference work for mathematical finance and will be indispensable to readers who need to find a quick introduction or reference to a specific topic, leading all the way to cutting edge material.


Bond and Money Markets

Bond and Money Markets

Author: Moorad Choudhry

Publisher: Butterworth-Heinemann

Published: 2003-07-04

Total Pages: 1152

ISBN-13: 0080574939

DOWNLOAD EBOOK

The Bond and Money Markets is an invaluable reference to all aspects of fixed income markets and instruments. It is highly regarded as an introduction and an advanced text for professionals and graduate students.Features comprehensive coverage of: * Government and Corporate bonds, Eurobonds, callable bonds, convertibles * Asset-backed bonds including mortgages and CDOs * Derivative instruments including futures, swaps, options, structured products* Interest-rate risk, duration analysis, convexity, and the convexity bias * The money markets, repo markets, basis trading, and asset/liability management * Term structure models, estimating and interpreting the yield curve * Portfolio management and strategies,total return framework, constructing bond indices * A stand alone reference book on interest rate swaps, the money markets, financial market mathematics, interest-rate futures and technical analysis * Includes introductory coverage of very specialised topics (for which one previously required several texts) such as VaR, Asset & liability management and credit derivatives * Combines accessible style with advanced level topics


Rethinking Valuation and Pricing Models

Rethinking Valuation and Pricing Models

Author: Carsten Wehn

Publisher: Academic Press

Published: 2012-12-17

Total Pages: 657

ISBN-13: 0124158889

DOWNLOAD EBOOK

It is widely acknowledged that many financial modelling techniques failed during the financial crisis, and in our post-crisis environment many techniques are being reconsidered. This single volume provides a guide to lessons learned for practitioners and a reference for academics. Including reviews of traditional approaches, real examples, and case studies, contributors consider portfolio theory; methods for valuing equities and equity derivatives, interest rate derivatives, and hybrid products; and techniques for calculating risks and implementing investment strategies. Describing new approaches without losing sight of their classical antecedents, this collection of original articles presents a timely perspective on our post-crisis paradigm. Highlights pre-crisis best classical practices, identifies post-crisis key issues, and examines emerging approaches to solving those issues Singles out key factors one must consider when valuing or calculating risks in the post-crisis environment Presents material in a homogenous, practical, clear, and not overly technical manner


Advanced Fixed-Income Valuation Tools

Advanced Fixed-Income Valuation Tools

Author: Narasimhan Jegadeesh

Publisher: John Wiley & Sons

Published: 1999-12-28

Total Pages: 438

ISBN-13: 9780471254195

DOWNLOAD EBOOK

Presenting the most advanced thinking on the topic, this book covers the latest valuation models and techniques. It addresses essential topics such as the subtleties of fixed-income mathematics, new approaches to modeling term structures, and the applications of fixed-income valuation on credit risk, mortgages, munis, and indexed bonds.


Stochastic Calculus for Finance II

Stochastic Calculus for Finance II

Author: Steven E. Shreve

Publisher: Springer Science & Business Media

Published: 2004-06-03

Total Pages: 586

ISBN-13: 9780387401010

DOWNLOAD EBOOK

"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM


Dynamic Asset Pricing Theory

Dynamic Asset Pricing Theory

Author: Darrell Duffie

Publisher: Princeton University Press

Published: 2010-01-27

Total Pages: 488

ISBN-13: 1400829208

DOWNLOAD EBOOK

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.


Asset Pricing

Asset Pricing

Author: John H. Cochrane

Publisher: Princeton University Press

Published: 2009-04-11

Total Pages: 560

ISBN-13: 1400829135

DOWNLOAD EBOOK

Winner of the prestigious Paul A. Samuelson Award for scholarly writing on lifelong financial security, John Cochrane's Asset Pricing now appears in a revised edition that unifies and brings the science of asset pricing up to date for advanced students and professionals. Cochrane traces the pricing of all assets back to a single idea--price equals expected discounted payoff--that captures the macro-economic risks underlying each security's value. By using a single, stochastic discount factor rather than a separate set of tricks for each asset class, Cochrane builds a unified account of modern asset pricing. He presents applications to stocks, bonds, and options. Each model--consumption based, CAPM, multifactor, term structure, and option pricing--is derived as a different specification of the discounted factor. The discount factor framework also leads to a state-space geometry for mean-variance frontiers and asset pricing models. It puts payoffs in different states of nature on the axes rather than mean and variance of return, leading to a new and conveniently linear geometrical representation of asset pricing ideas. Cochrane approaches empirical work with the Generalized Method of Moments, which studies sample average prices and discounted payoffs to determine whether price does equal expected discounted payoff. He translates between the discount factor, GMM, and state-space language and the beta, mean-variance, and regression language common in empirical work and earlier theory. The book also includes a review of recent empirical work on return predictability, value and other puzzles in the cross section, and equity premium puzzles and their resolution. Written to be a summary for academics and professionals as well as a textbook, this book condenses and advances recent scholarship in financial economics.


Mathematical and Statistical Methods for Actuarial Sciences and Finance

Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author: Marco Corazza

Publisher: Springer

Published: 2018-07-17

Total Pages: 465

ISBN-13: 3319898248

DOWNLOAD EBOOK

The interaction between mathematicians, statisticians and econometricians working in actuarial sciences and finance is producing numerous meaningful scientific results. This volume introduces new ideas, in the form of four-page papers, presented at the international conference Mathematical and Statistical Methods for Actuarial Sciences and Finance (MAF), held at Universidad Carlos III de Madrid (Spain), 4th-6th April 2018. The book covers a wide variety of subjects in actuarial science and financial fields, all discussed in the context of the cooperation between the three quantitative approaches. The topics include: actuarial models; analysis of high frequency financial data; behavioural finance; carbon and green finance; credit risk methods and models; dynamic optimization in finance; financial econometrics; forecasting of dynamical actuarial and financial phenomena; fund performance evaluation; insurance portfolio risk analysis; interest rate models; longevity risk; machine learning and soft-computing in finance; management in insurance business; models and methods for financial time series analysis, models for financial derivatives; multivariate techniques for financial markets analysis; optimization in insurance; pricing; probability in actuarial sciences, insurance and finance; real world finance; risk management; solvency analysis; sovereign risk; static and dynamic portfolio selection and management; trading systems. This book is a valuable resource for academics, PhD students, practitioners, professionals and researchers, and is also of interest to other readers with quantitative background knowledge.


Dynamic Term Structure Modeling

Dynamic Term Structure Modeling

Author: Sanjay K. Nawalkha

Publisher: John Wiley & Sons

Published: 2007-05-23

Total Pages: 722

ISBN-13: 0470140062

DOWNLOAD EBOOK

Praise for Dynamic Term Structure Modeling "This book offers the most comprehensive coverage of term-structure models I have seen so far, encompassing equilibrium and no-arbitrage models in a new framework, along with the major solution techniques using trees, PDE methods, Fourier methods, and approximations. It is an essential reference for academics and practitioners alike." --Sanjiv Ranjan Das Professor of Finance, Santa Clara University, California, coeditor, Journal of Derivatives "Bravo! This is an exhaustive analysis of the yield curve dynamics. It is clear, pedagogically impressive, well presented, and to the point." --Nassim Nicholas Taleb author, Dynamic Hedging and The Black Swan "Nawalkha, Beliaeva, and Soto have put together a comprehensive, up-to-date textbook on modern dynamic term structure modeling. It is both accessible and rigorous and should be of tremendous interest to anyone who wants to learn about state-of-the-art fixed income modeling. It provides many numerical examples that will be valuable to readers interested in the practical implementations of these models." --Pierre Collin-Dufresne Associate Professor of Finance, UC Berkeley "The book provides a comprehensive description of the continuous time interest rate models. It serves an important part of the trilogy, useful for financial engineers to grasp the theoretical underpinnings and the practical implementation." --Thomas S. Y. Ho, PHD President, Thomas Ho Company, Ltd, coauthor, The Oxford Guide to Financial Modeling