外来品期权定价与高级Levy模型(英文原版进口)

2005-08-26  

John Wiley*  

SCHOUTENS  

320  

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.

ContributorsPrefaceAbout the EditorsAbout the Contributors1 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 References2 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 Conclusions3 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 References4 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 References5 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 References6 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 References7 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 References8 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 References9 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 references10 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 References11 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 References12 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 References13 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 References14 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 ReferencesIndex

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