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

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

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.

- 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
- 1.6 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
- 2.2 The credit market and its derivatives
- 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
- 3.4 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
- 4.2 Exotic stock options
- 4.3 Methods for European options: analytic formulation
- 4.4 Methods for European options: finite differences (FD)
- 4.5 Methods for European options: Monte-Carlo sampling (MCS)
- 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
- 5.2 Credit derivatives
- 5.3 Methods for bonds and derivatives: finite elements (FEM)
- 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
- 6.2 Methods for American options: finite elements (FEM)
- 6.3 Computer quiz
- 6.4 Exercises
- 6.5 Further reading and links
- 6.6 Quick intermediate evaluation form

- 7 EXTREMAL EVENTS

- 8 MULTI-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