This guide requires mathematical background knowledge.

Table of Contents

1  Financial Derivatives
1.1  Discrete time models
1.1.1  Strategies of investment
1.1.2  Admissible strategies and arbitrage
1.1.3  Martingales and opportunities of arbitrage
1.1.4  Complete markets and option pricing
1.1.5  American options
1.1.6  The optimal stopping problem
1.1.7  Application to American options
1.2  Continuous-time models
1.2.1  Continuous-time Martingales
1.2.2  Stochastic Integration
1.2.3  Itˆo’s Calculus
1.2.4  The Girsanov theorem
1.2.5  The Black-Scholes model
1.2.6  Multidimensional Black-Scholes model with continuous div-idends
1.2.7  Currency options
1.2.8  Stochastic volatility
1.2.9  Fourier methods for pricing

2  Interest rates models
2.1  Basic facts
2.1.1  The yield curve
2.1.2  Yield curve for a random future
2.1.3  Interest rates
2.1.4  Bonds with coupons, swaps, caps and floors
2.2  A general framework for short rates
2.3  Options on bonds
2.4  Short rate models
12.4.1  Inversion of the yield curve
2.4.2  Affine term structures
2.4.3  The Vasicek model
2.4.4  The Ho-Lee model
2.4.5  The CIR model
2.4.6  The Hull-White model
2.5  Forward rate models
2.5.1  The Musiela equation
2.6  Change of numeraire. The forward measure
2.7  Market models
2.7.1  A market model for Swaptions
2.7.2  A LIBOR market model
2.7.3  A market model for caps
2.8  Miscelanea
2.8.1  Forwards and Futures
2.8.2  Stock options