O'Reilly logo

A Workout in Computational Finance by Michael Aichinger, Andreas Binder

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Contents

Acknowledgements

About the Authors

1 Introduction and Reading Guide

2 Binomial Trees

2.1 Equities and Basic Options

2.2 The One Period Model

2.3 The Multiperiod Binomial Model

2.4 Black-Scholes and Trees

2.5 Strengths and Weaknesses of Binomial Trees

2.5.1 Ease of Implementation

2.5.2 Oscillations

2.5.3 Non-recombining Trees

2.5.4 Exotic Options and Trees

2.5.5 Greeks and Binomial Trees

2.5.6 Grid Adaptivity and Trees

2.6 Conclusion

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

3.3 Finite Differences

3.4 Time Discretization

3.5 Stability Considerations

3.6 Finite Differences and the Heat Equation

3.6.1 Numerical Results

3.7 Appendix: Error Analysis

4 Mean Reversion and Trinomial Trees

4.1 Some Fixed Income Terms

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

4.5 Trinomial Trees

5 Upwinding Techniques for Short Rate Models

5.1 Derivation of a PDE for Short Rate Models

5.2 Upwind Schemes

5.2.1 Model Equation

5.3 A Puttable Fixed Rate Bond under the Hull-White One Factor Model

5.3.1 Bond Details

5.3.2 Model Details

5.3.3 Numerical Method

5.3.4 An Algorithm in Pseudocode

5.3.5 Results

6 Boundary, Terminal and Interface Conditions and their Influence

6.1 Terminal Conditions for Equity Options

6.2 Terminal ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required