Financial Modeling: Options, Swaps and Derivatives André Jaun, NADA, Royal Institute of Technology, Stockholm Register now for the Netuniversity edition (Sep 19 - Dec 15, 2005)

This is the web edition of the distance learning courses taught at the Royal Institute of Technology in Stockholm (KTH course 2D5244, 4 points), the University of Adelaide (Masters in Applied Finance programme), the Swedish Netuniversity (KTH course 2D4282, 4 points) and independent learners from outside Sweden. The target is to familiarize the participants with the methodology used in financial engineering to manage the investment risks in stock and bond markets.
The material has been designed so that it can be studied at different levels depending on the mathematical background and the ambition of every participant: with little algebra, practitionners get a practical understanding of the option payoff dynamics using virtual market experiments in a java-powered web browser. At a more advanced level, graduates from quantitative fields learn how to use stochastic calculus to formulate financial models and to implement numerical solutions in the VMARKET applet: be patient, it takes about 15 secs to load with a 56K modem...

Hedging strategies involving shares, bonds and their derivatives are discussed, starting from no arbitrage arguments to derive PDEs such as the celebrated Black-Scholes equation. Solutions obtained using finite differences, finite elements and Monte-Carlo methods are compared with each other and provide the background to implement more sophisticated models. Assignments are an essential part of the learning process: they are submitted from the web browser and automatically compiled into web pages where the students explain with words, equations and programs how to derive, implement and run their own numerical schemes.

Table of contents

• Contents
• 1 INTRODUCTION
  • 1.1 How to study this course at 3 levels: the meaning of
  • 1.2 Capital and markets
  • 1.3 The risk and return from conventional assets
  • 1.4 Modern portfolio theory and basic risk management strategies
  • 1.5 Historical data and modeling
    • 1.5.1 Drift and volatility of market prices
    • 1.5.2 Moving averages: UWMA, EWMA, GARCH
    • 1.5.3 Maximum likelihood estimate of parameters
  • 1.6 Computer quiz
  • 1.7 Exercises
  • 1.8 Further reading and links
  • 1.9 Quick intermediate evaluation form
  
  
• 2 A VARIETY OF SECURITIES
  • 2.1 The stock market and its derivatives
    • 2.1.1 Shares and market indices
    • 2.1.2 Forward contract and futures markets
    • 2.1.3 Plain vanilla options
    • 2.1.4 Exotic options
    • 2.1.5 LEAPS and warrants
  • 2.2 The credit market and its derivatives
    • 2.2.1 Interest rates: treasury note, LIBOR, credit spread
    • 2.2.2 Underlying discount bonds and forward rates
    • 2.2.3 Interest rate swaps and forward rate agreements
    • 2.2.4 Bond options: caps, floors and swaptions
  • 2.3 Convertible bonds
  • 2.4 Hedging parameters, portfolio sensitivity
  • 2.5 Computer quiz
  • 2.6 Exercises
  • 2.7 Further reading and links
  • 2.8 Quick intermediate evaluation form
  
  
• 3 FORECASTING WITH UNCERTAINTY
  • 3.1 Option pricing for dummies
  • 3.2 Simple valuation model using binomial trees
  • 3.3 Improved model using stochastic calculus
    • 3.3.1 Wiener process and martingales
    • 3.3.2 Itô lemma
    • 3.3.3 Evaluate an expectancy or eliminate the uncertainty
  • 3.4 Hedging an option with the underlying (Black-Scholes)
  • 3.5 Hedging a bond with another bond (Vasicek)
  • 3.6 Computer quiz
  • 3.7 Exercises
  • 3.8 Further reading and links
  • 3.9 Quick intermediate evaluation form
  
  
• 4 EUROPEAN OPTION PAYOFF DYNAMICS
  • 4.1 Plain vanilla stock options
    • 4.1.1 The European Black-Scholes model for dummies
    • 4.1.2 Parameters illustrated with VMARKET experiments
    • 4.1.3 Application, time value and implied volatility
  • 4.2 Exotic stock options
    • 4.2.1 Binary options
    • 4.2.2 Barrier options
  • 4.3 Methods for European options: analytic formulation
    • 4.3.1 Transformation to log-normal variables
    • 4.3.2 Solution of the normalized diffusion equation
    • 4.3.3 Black-Scholes formula
  • 4.4 Methods for European options: finite differences (FD)
    • 4.4.1 Naive implementation using financial variables
    • 4.4.2 Improved scheme using log-normal variables
  • 4.5 Methods for European options: Monte-Carlo sampling (MCS)
    • 4.5.1 Forecast possible realizations of the underlying asset
    • 4.5.2 Expected value of an option from sampled data
  • 4.6 Computer quiz
  • 4.7 Exercises
  • 4.8 Further reading and links
  • 4.9 Quick intermediate evaluation form
  
  
• 5 BONDS, SWAPS AND DERIVATIVES
  • 5.1 Discound bonds
    • 5.1.1 Term structure models for dummies
    • 5.1.2 Parameters illustrated with VMARKET experiments
  • 5.2 Credit derivatives
    • 5.2.1 Vanilla swaps
    • 5.2.2 Cap-/floorlets
  • 5.3 Methods for bonds and derivatives: finite elements (FEM)
    • 5.3.1 The Vasicek model for a bond
    • 5.3.2 Extensions for derivatives
  • 5.4 Computer quiz
  • 5.5 Exercises
  • 5.6 Further reading and links
  • 5.7 Quick intermediate evaluation form
  
  
• 6 AMERICAN OPTION PAYOFF DYNAMICS
  • 6.1 American stock options
    • 6.1.1 The American Black-Scholes model for dummies
    • 6.1.2 Parameters illustrated with VMARKET experiments
    • 6.1.3 Application
  • 6.2 Methods for American options: finite elements (FEM)
    • 6.2.1 The Black-Scholes equation for American options
    • 6.2.2 Solution of the variational inequality using finite elements
  • 6.3 Computer quiz
  • 6.4 Exercises
  • 6.5 Further reading and links
  • 6.6 Quick intermediate evaluation form
  
  
• 7 EXTREMAL EVENTS
  • 7.1 Basel accord on banking
  • 7.2 Value at risk (VaR)
  • 7.3 Copulas for risk management
  
  
• 8 MULTI-FACTOR MODELS
  • 8.1 Principal components analysis
  • 8.2 Martingales and measures
  • 8.3 Two factor models
  
  
• 9 LEARNING LABORATORY ENVIRONEMENT
  • 9.1 Typesetting with TEX
  • 9.2 Programming in JAVA
  • 9.3 VMarket parameters and preset in HTML
  • 9.4 Quick intermediate evaluation form
  
  
• 10 APPENDIX
  • 10.1 Glossary of keywords
  • 10.2 Notation and symbols
  • 10.3 Final interactive evaluation form