Financial Derivatives and Market Risk Management
by JIŘÍ WITZANY
2011
Contents
1. Introduction
2. Forwards and Futures
3. Interest Rate Derivatives
4. Option Markets, Valuation and Hedging
5. Market Risk Measurement and Management
6. Interest Rate Options
7. Interest Rate Modeling
8. Exotic Options and Alternative Stochastic Models
Appendix : Elementary Stochastic Calculus
The goal of these lecture notes is to provide English written and accessible, introductory and
advanced text on derivatives and market risk management for the Financial Engineering
Master’s degree program students, and for other students attending derivatives courses at the
University of Economics in Prague. The first part of the lecture notes follows the content of
the Financial Derivatives (1BP 426) course. After an overview of basic derivatives types and
their classification, it explains in detail trading mechanics and pricing of forwards, futures,
and swaps. The last chapter gives an introduction to financial stochastic modeling applied to
Black-Scholes option pricing, and risk management of options. The approach is based on the
concept of binomial trees extended to the continuous time modeling using the notion of
infinitesimals. The theoretical concepts are accompanied with many examples and figures that
aim to emphasize practical issues of derivatives trading. The second, separate, part of the
lecture notes, related to the course Financial Derivatives II (1BP 451), will cover more
advanced topics. It will start with a chapter focusing on market risk measurement and
management techniques. The second key topic will be stochastic interest rate modeling and
extensions of the Black-Scholes model to interest rate derivatives pricing. Finally, we will
analyze shortcomings of the geometric Brownian motion model assuming normal returns and
study various more advanced models like the jump-diffusion, or stochastic volatility, and
other models that aim to be more faithful with respect to observable financial data.