外来品期权定价与高级Levy模型EXOTIC OPTION PRICING AND ADVANCED LéVY MODELS 下载 pdf 百度网盘 epub 免费 2025 电子书 mobi 在线

Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black–Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field.

作者简介：ANDREAS KYPRIANOU has a degree in Mathematics from Oxford University and a PhD in Probability Theory from Sheffield University. He has held academic positions in Mathematics and Statistics departments at The London School of Economics, Edinburgh University, Utrecht University and, currently, Heriot Watt University. He has also worked for nearly two years as a research mathematician with Shell International Exploration and Production. His research interests are focused on pure and applied probability with recent focus on Lévy processes. He has taught a range of courses on Probability Theory, Stochastic Analysis, Financial Stochastics and Lévy Processes for the Amsterdam-Utrecht Masters programme in Stochastics and Financial Mathematics and the MSc programme in Financial Mathematics at Edinburgh.

Contributors

Preface

About the Editors

About the Contributors

1 Levy Processes in Finance Distinguished by their Coarse and Fine Path Properties Andreas EKyprianou and RLoeffen

1.1 Introduction

1.2 Levy Processes

1.3 Examples of Levy Processes in finance

1.4 Path properties

1.5 Examples revisited

1.6 Conclusions

References

2 Simulation Methods with Levy Processes Nick Webber

2.1 Introduction

2.2 Modelling price and rate movements

2.3 A basis for a numerical approach

2.4 Constructing bridges for Levy Processes

2.5 Valuing discretely reset path-dependant options

2.6 Valuing continuously reset path-dependent options

2.7 Conclusions

3 Risks in Returns: A Pure Jump Perspective Helyette Geman and Dilip BMadan

3.1 Introduction

3.2 CGMY model details

3.3 Estimation details

3.4 Estimation results

3.5 Conclusions

References

4 Model Risk for Exotic and Moment Derivatives Wim Schoutens, Erwin Simons and Jurgen Tistaert

4.1 Introduction

4.2 The models

4.3 Calibration

4.4 Simulation

4.5 Pricing of exotic options

4.6 Pricing of moment derivatives

4.7 Conclusions

References

5 Symmetries and Pricing of Exotic Options in Levy Models Ernst Eberlein and Antonis Papapantoleon

5.1 Introduction

5.2 Model and assumptions

5.3 General description of the method

5.4 Vanilla options

5.5 Exotic options

5.6 Margrabe-type options

References

6 Static Hedging of Asian Options Under Stochastic Volatility Models using Fast Fourier Transform Hansjorg Albrecher and Wim Schoutens

6.1 Introduction

6.2 Stochastic volatility models

6.3 Static hedging of Asian options

6.4 Numerical Implementation

6.5 Numerical illustrations

6.6 A model-independent static super-hedge

6.7 Conclusions

References

7 Impact of Market Crises on Real Options Pauline Barrieu and Nadine Bellamy

7.1 IOntroduction

7.2 The model

7.3 The real option characteristics

7.4 Optimal discount rate and average waiting time

7.5 Robustness of the inverstment decision characters

7.6 Contiuos models versus discontinuous model

7.7 Conclusions

References

8 Moment Derivatives and Levy-type Market Completion Jose Manuel Corcuera, David Nualart and Wim Schoutens

8.1 Introduction

8.2 Market completuion in the descrete-time setting

8.3 The Levy market

8.4 Enlarging the Levy market model

8.5 Arbitrage

8.6 Optimal portfolios

References

9 Pricing Perpetual American Options Driven by Spectrally One-sided Levy Processes Terence Chan

9.1 Introduction

9.2 First-passage distributions and other results for spectrally positive Levy

9.3 Description of the model, basic definitions and notations

9.4 A renewal equation approach to pricing

9.5 Explicit pricing formulae for American puts

9.6 Some specific examples

Appendix: use of fast fourier transform

References

Epilogue

Further references

10 On Asian Options of American Type Goran Peskir and Nadia Uys

10.1 Introduction

10.2 Formulation of the problem

10.3 The result and proof

10.4 Remarks on numerics

Appendix

References

11 Why be Backward? Forward Equations for American Options Peter Carr and Ali Hirsa

11.1 Introduction

11.2 Reveiw of the backward free boundary problem

11.3 Stationarity and domain extension in the maturity direction

11.4 Additivity and domain extension in the strike direction

11.5 The forward free boundary problem

11.6 Summary and future research

Appendix: Discretization of forward equation for American options

References

12 Numerical Valuation of American Options Under the CGMY Process Ariel Almendral

12.1 Introduction

12.2 The CGMY process as a Levy process

12.3 Numerical Valuation of the American CGMY price

12.4 Numerical experiments

Appendix: Analytic formula for European option prices

References

13 Convertible Bonds: Financial Derivatives of Game Type Jan Kallsen and Christoph Kuhn

13.1 Introduction

13.2 No-arbitrage pricing for game contigent claims

13.3 Convertible bonds

13.4 Conclusions

References

14 The Spread Option Optimal Stopping Game Pavel VGapeev

14.1 Introduction

14.2 Formulation of the problem

14.3 Solution of the free-boundary problem

14.4 Main result and proof

14.5 Conclusions

References

Index

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书籍介绍

Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Levy process. Working with Levy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Levy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Levy markets, written by leading scientists in this field. In recent years, Levy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward