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The Mathematics of Derivatives
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The Mathematics of Derivatives

The Mathematics of Derivatives

Tools for Designing Numerical Algorithms

Robert L. Navin - Collection Wiley Finance

208 pages, parution le 29/01/2007

Résumé

In the dynamic field of finance, where mathematics is playing an ever-greater role in decision making, understanding the mathematical underpinnings and implications of derivatives is an important endeavor.

Nobody knows this better than author Robert Navin, whose detailed knowledge of derivatives has allowed him to excel over the course of his financial career-as well as help those around him quickly grasp the mathematical techniques behind the modeling of derivatives. Now, in The Mathematics of Derivatives, he shares his expertise and experience with you.

Filled with in-depth insights and practical advice, The Mathematics of Derivatives provides individuals involved in this industry-whether you're a quant-in-training with a background in economics or a software designer creating financial programs-with the information they need to succeed.

Divided into two comprehensive parts, this well-rounded resource outlines the models-and the math-used to analyze the trading and risks of derivatives in Part One and then challenges you to master these methods through a variety of exercises in Part Two.

An array of topics are covered, including:

  • The Black-Scholes formula with modifications as well as more general ideas behind the derivation of the Black-Scholes formula
  • Relevant mathematical tools-from distribution and integration definitions to n-Dimensional Jacobians, Path Integrals, and the Central Limit Theorem
  • Stochastic processes and their applications to finance
  • Numerical algorithmic methods for solving parabolic partial differential equations (PDEs)
  • The simple default probability approach to credit derivatives
  • The Heath-Jarrow-Morton (HJM) model, as well as some specific examples of modeling derivatives, such as convertible bonds and collateralized debt obligations

With the information illustrated throughout these pages, you'll be able to implement the risk-neutral pricing paradigm correctly, design models of real-world processes using stochastic calculus, convert such models into a risk-neutral pricing equation with boundary conditions, numerically solve these equations with great accuracy, and much more.

In order to fully understand the pricing, hedging, and risk management issues associated with derivatives, you must first become familiar with the mathematical formalism that underlies them. Written in a straightforward and accessible style, The Mathematics of Derivatives provides you with a solid foundation in this field-and an opportunity to succeed in today's turbulent markets.

L'auteur - Robert L. Navin

ROBERT L. NAVIN founded Real Time Risk Systems LLC in July 2004. Prior to this, he helped set up a hedge fund in 2002 that grew to more than $1 billion in assets under management during its first year. Navin was previously at Highbridge Capital Management as head of quantitative analysis from 1997 to 2002. He graduated with an MS and a PhD in theoretical particle physics from the California Institute of Technology in 1993.

Sommaire

  • The Models.
    • Introduction to the Techniques of Derivative Modeling.
    • Preliminary Mathematical Tools.
    • Stochastic Calculus.
    • Applications of Stochastic Calculus to Finance.
    • From Stochastic Processes Formalism to Differential Equation Formalism.
    • Understanding the Black-Scholes Equation.
    • Interest Rate Hedging.
    • Interest Rate Derivatives: HJM Models.
    • Credit Spreads.
    • Specific Models.
  • Exercises and Solutions.
    • Exercises.
    • Solutions.
Voir tout
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Caractéristiques techniques

  PAPIER
Éditeur(s) Wiley
Auteur(s) Robert L. Navin
Collection Wiley Finance
Parution 29/01/2007
Nb. de pages 208
Format 16 x 23,7
Couverture Relié
Poids 390g
Intérieur Noir et Blanc
EAN13 9780470047255
ISBN13 978-0-470-04725-5

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