Stochastic calculus for Finance : continuous-time models . II,

목차 (Table of Contents)

• 자료제공 :
• 1 General Probability Theory
• 1.1 In.nite Probability Spaces
• 1.2 Random Variables and Distributions
• 1.3 Expectations
• 1.4 Convergence of Integrals
• 1.5 Computation of Expectations
• 1.6 Change of Measure
• 1.7 Summary
• 1.8 Notes
• 1.9 Exercises 2 Information and Conditioning
• 2.1 Information and s-algebras
• 2.2 Independence
• 2.3 General Conditional Expectations
• 2.4 Summary
• 2.5 Notes
• 2.6 Exercises 3 Brownian Motion
• 3.1 Introduction
• 3.2 Scaled Random Walks
• 3.2.1 Symmetric Random Walk
• 3.2.2 Increments of Symmetric Random Walk
• 3.2.3 Martingale Property for Symmetric Random Walk
• 3.2.4 Quadratic Variation of Symmetric Random Walk
• 3.2.5 Scaled Symmetric Random Walk
• 3.2.6 Limiting Distribution of Scaled Random Walk
• 3.2.7 Log-Normal Distribution as Limit of Binomial Model
• 3.3 Brownian Motion
• 3.3.1 Definition of Brownian Motion
• 3.3.2 Distribution of Brownian Motion
• 3.3.3 Filtration for Brownian Motion
• 3.3.4 Martingale Property for Brownian Motion
• 3.4 Quadratic Variation
• 3.4.1 First-Order Variation
• 3.4.2 Quadratic Variation
• 3.4.3 Volatility of Geometric Brownian Motion
• 3.5 Markov Property
• 3.6 First Passage Time Distribution
• 3.7 Re.ection Principle
• 3.7.1 Reflection Equality
• 3.7.2 First Passage Time Distribution
• 3.7.3 Distribution of Brownian Motion and Its Maximum
• 3.8 Summary
• 3.9 Notes
• 3.10 Exercises 4 Stochastic Calculus
• 4.1 Introduction
• 4.2 It o's Integral for Simple Integrands
• 4.2.1 Construction of the Integral
• 4.2.2 Properties of the Integral
• 4.3 It o's Integral for General Integrands
• 4.4 It o-Doeblin Formula
• 4.4.1 Formula for Brownian Motion
• 4.4.2 Formula for It o Processes
• 4.4.3 Examples
• 4.5 Black-Scholes-Merton Equation
• 4.5.1 Evolution of Portfolio Value
• 4.5.2 Evolution of Option Value
• 4.5.3 Equating the Evolutions
• 4.5.4 Solution to the Black-Scholes-Merton Equation
• 4.5.5 TheGreeks
• 4.5.6 Put-Call Parity
• 4.6 Multivariable Stochastic Calculus
• 4.6.1 Multiple Brownian Motions
• 4.6.2 It o-Doeblin Formula for Multiple Processes
• 4.6.3 Recognizing a Brownian Motion
• 4.7 Brownian Bridge
• 4.7.1 Gaussian Processes
• 4.7.2 Brownian Bridge as a Gaussian Process
• 4.7.3 Brownian Bridge as a Scaled Stochastic Integral
• 4.7.4 Multidimensional Distribution of Brownian Bridge
• 4.7.5 Brownian Bridge as Conditioned Brownian Motion
• 4.8 Summary
• 4.9 Notes
• 4.10 Exercises 5 Risk-Neutral Pricing
• 5.1 Introduction
• 5.2 Risk-Neutral Measure
• 5.2.1 Girsanov's Theorem for a Single Brownian Motion
• 5.2.2 Stock Under the Risk-Neutral Measure
• 5.2.3 Value of Portfolio Process Under the Risk-Neutral Measure
• 5.2.4 Pricing Under the Risk-Neutral Measure
• 5.2.5 Deriving the Black-Scholes-Merton Formula
• 5.3 Martingale Representation Theorem
• 5.3.1 Martingale Representation with One Brownian Motion
• 5.3.2 Hedging with One Stock
• 5.4 Fundamental Theorems of Asset Pricing
• 5.4.1 Girsanov and Martingale Representation Theorems
• 5.4.2 Multidimensional Market Model
• 5.4.3 Existence of Risk-Neutral Measure
• 5.4.4 Uniqueness of the Risk-Neutral Measure
• 5.5 Dividend-Paying Stocks
• 5.5.1 Continuously Paying Dividend
• 5.5.2 Continuously Paying Dividend with Constant Coeffcients
• 5.5.3 Lump Payments of Dividends
• 5.5.4 Lump Payments of Dividends with Constant Coeffcients
• 5.6 Forwards and Futures
• 5.6.1 Forward Contracts
• 5.6.2 Futures Contracts
• 5.6.3 Forward-Futures Spread
• 5.7 Summary
• 5.8 Notes
• 5.9 Exercises 6 Connections with Partial Differential Equations
• 6.1 Introduction
• 6.2 Stochastic Differential Equations
• 6.3 The Markov Property
• 6.4 Partial Differential Equations
• 6.5 Interest Rate Models
• 6.6 Multidimensional Feynman-Kac Theorems
• 6.7 Summary
• 6.8 Notes
• 6.9 Exercises 7 Exotic Options
• 7.1 Introduction