Contents
1 Introduction and Reading Guide
2.1 Equities and Basic Options
2.3 The Multiperiod Binomial Model
2.5 Strengths and Weaknesses of Binomial Trees
2.5.4 Exotic Options and Trees
2.5.5 Greeks and Binomial Trees
2.5.6 Grid Adaptivity and Trees
3 Finite Differences and the Black-Scholes PDE
3.1 A Continuous Time Model for Equity Prices
3.2 Black-Scholes Model: From the SDE to the PDE
3.6 Finite Differences and the Heat Equation
4 Mean Reversion and Trinomial Trees
4.1.1 Interest Rates and Compounding
4.1.2 Libor Rates and Vanilla Interest Rate Swaps
4.2 Black76 for Caps and Swaptions
4.3 One-Factor Short Rate Models
4.3.1 Prominent Short Rate Models
4.4 The Hull-White Model in More Detail
5 Upwinding Techniques for Short Rate Models
5.1 Derivation of a PDE for Short Rate Models
5.3 A Puttable Fixed Rate Bond under the Hull-White One Factor Model
5.3.4 An Algorithm in Pseudocode
6 Boundary, Terminal and Interface Conditions and their Influence
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