Preface
Chapter 1.Financial Markets and Derivatives
1.1.Financial Markets
1.2.Derivatives
1.3.Exercise
Chapter 2.Binomial Model
2.1.Binomial or CRR Model
2.2.Pricing a European Contingent Claim
2.3.Pricing an American Contingent Claim
2.4.Exercises
Chapter 3.Finite Market Model
3.1.Definition of the Finite Market Model
3.2.First Fundamental Theorem of Asset Pricing
3.3.Second Fundamental Theorem of Asset Pricing
3.4.Pricing European Contingent Claims
3.5.Incomplete Markets
3.6.Separating Hyperplane Theorem
3.7.Exercises
Chapter 4.Black—Scholes Model
4.1.Preliminaries
4.2.Black—Scholes Model
4.3.Equivalent Martingale Measure
4.4.European Contingent Claims
4.5.Pricing European Contingent Claims
4.6.European Call Option — Black—Scholes Formula
4.7.American Contingent Claims
4.8.American Call Option
4.9.American Put Option
4.10.Exercises
Chapter 5.Multi—dimensional Black—Scholes Model
5.1.Preliminaries
5.2.Multi—dimensional Black—Seholes Model
5.3.First Fundamental Theorem of Asset Pricing
5.4.Form of Equivalent Local Martingale Measures
5.5.Second Fundamental Theorem of Asset Pricing
5.6.Pricing European Contingent Claims
5.7.Incomplete Markets
5.8.Exercises
Appendix A.Conditional Expectation and LP—Spaces
Appendix B.Discrete Time Stochastic Processes
Appendix C.Continuous Time Stochastic Processes
Appendix D.Brownian Motion and Stochastic Integration
D.1.Brownian Motion
D.2.Stochastic Integrals （with respect to Brownian motion）
D.3.Ito Process
D.4.Ito Formula
D.5.Girsanov Transformation
D.6.Martingale Representation Theorem
Bibliography
Index
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