LIBOR and Swap Market Models Monte Carlo Simulations

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学习LMM模型的好材料。
LIBOR and Swap Market Models for Pricing Interest Rate Derivatives Monte Carlo Simulations


Contents
Dedication i
Acknowledgements ii
Abstract iii
Introduction 1
1 Elements of Financial Calculus 2
1.1 Conditional Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Conditioning on a random variable . . . . . . . . . . . . . . . . . . 2
1.1.2 Conditioning on a - eld . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Martingales in Continuous Time . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Brownian Motion and some Properties . . . . . . . . . . . . . . . . . . . . 6
1.4 It^o Integral and It^o Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Stochastic Di erential Equations . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 Cameron-Martin-Girsanov Theorem . . . . . . . . . . . . . . . . . . . . . . 12
2 LIBOR Market Models 14
2.1 Stochastic Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.1 Simple and Stochastic Interest Rates . . . . . . . . . . . . . . . . . 15
2.1.2 Forward Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 LIBOR Market Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Forward LIBOR Rate Processes . . . . . . . . . . . . . . . . . . . . 17
2.2.2 LIBOR Market Models . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 LIBOR Market Models under the Terminal Measure . . . . . . . . . 19
2.3 Caps and Caplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 Cap Value Process under the Terminal Measure . . . . . . . . . . . 22
3 Swap Market Models 23
3.1 Swaps and Swaptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 Valuation of Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.2 Forward Swap Rates . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.3 Swaption Pricing in a Forward measure . . . . . . . . . . . . . . . . 26
3.2 Swap Market Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Swap Market Models under the Terminal Measure . . . . . . . . . . 28
4 Monte Carlo Simulations 32
4.1 Monte Carlo Expectation, Monte Carlo Variance . . . . . . . . . . . . . . . 32
4.2 Monte Carlo Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Monte Carlo Method for LIBOR Market Models . . . . . . . . . . . . . . . 34
4.3.1 Implementation of the Method . . . . . . . . . . . . . . . . . . . . . 34
4.3.2 Simulation Results and Application . . . . . . . . . . . . . . . . . . 35
Conclusion 38
Bibliography 39
Appendices 39

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关键词：Monte Carlo Simulations Simulation ulation models Monte Carlo Simulations

狠狠心买了，钱哗哗的花啊

你也研究LMM模型吗？有空一起探讨，校准程序比较难实现啊。这个文档有点matlab的实现代码

目录看起来不错，不知道内容如何

受益匪浅！
想知道楼主现在还玩这个吗？