N.-Y.: Wiley. 2006. - 208p.
Пособие по методам расчёта стоимости производных финансовых
инструментов. Приводятся основные сведения о теории вероятностей,
стохастическом исчислении, дифференциальных уравнениях в частных
производных применительно к расчёту деривативов, начиная от
опционов по Блэку-Шоулсу, затем к хеджированию процентных ставок,
кредитным спрэдам и другим моделям. Вторая часть включает
упражнения с решениями. Дополнительные математические сведения
вынесены в приложения.
Для изучающих финансовую математику и деривативы. Contents
Preface.
Acknowledgments.
The Models.
Introduction to the Techniques of Derivative Modeling.
Preliminary Mathematical Tools.
Stochastic Calculus.
Applications of Stochastic Calculus to Finance.
From Stochastic Processes Formalism to Differential Equation Formalism.
Understanding the Black-Scholes Equation.
Interest Rate Hedging.
Interest Rate Derivatives: HJM Models.
Differential Equations, Boundary Conditions, and Solutions.
Credit Spreads.
Specific Models.
Exercises and Solutions.
Exercises.
Solutions.
Appendix. Central Limit Theorem-Plausibility Argument.
Appendix. Solving for the Green’s Function of the Black-Scholes Equation.
Appendix. Expanding the von Neumann Stability Mode for the Discretized Black-Scholes Equation.
Appendix. Multiple Bond Survival Probabilities Given Correlated Default Probability Rates.
References.
Index.
Для изучающих финансовую математику и деривативы. Contents
Preface.
Acknowledgments.
The Models.
Introduction to the Techniques of Derivative Modeling.
Preliminary Mathematical Tools.
Stochastic Calculus.
Applications of Stochastic Calculus to Finance.
From Stochastic Processes Formalism to Differential Equation Formalism.
Understanding the Black-Scholes Equation.
Interest Rate Hedging.
Interest Rate Derivatives: HJM Models.
Differential Equations, Boundary Conditions, and Solutions.
Credit Spreads.
Specific Models.
Exercises and Solutions.
Exercises.
Solutions.
Appendix. Central Limit Theorem-Plausibility Argument.
Appendix. Solving for the Green’s Function of the Black-Scholes Equation.
Appendix. Expanding the von Neumann Stability Mode for the Discretized Black-Scholes Equation.
Appendix. Multiple Bond Survival Probabilities Given Correlated Default Probability Rates.
References.
Index.