Financial mathematics : from discrete to continuous time /: from discrete to continuous time. (2022)

• Record Type: Book
• Further Information: Note: Kevin J. Hastings.
• Authors: Hastings, Kevin J, 1955-
• Contents: Chapter 1 - Review of Preliminaries 1.1. Risky Assets 1.1.1. Single and Multiple Discrete Time Periods 1.1.2. Continuous-Time Processes 1.1.3. Martingales 1.2. Risk Aversion and Portfolios of Assets 1.2.1. Risk Aversion Constant 1.2.2. The Portfolio Problem 1.3. Expectation, Variance, and Covariance 1.3.1. One Variable Expectation 1.3.2. Expectation for Multiple Random Variables 1.3.3. Variance of a Linear Combination 1.4. Simple Portfolio Optimization 1.5. Derivative Assets and Arbitrage 1.5.1. Futures 1.5.2. Arbitrage and Futures 1.5.3. Options 1.6. Valuation of Derivatives in Single Time Period 1.6.1. Replicating Portfolios 1.6.2. Risk-Neutral Valuation Chapter 2 - More on Portfolio Optimization; Capital Market Theory 2.1. Portfolio Optimization with Multiple Assets 2.1.1. Lagrange Multipliers 2.1.1. Qualitative Behavior 2.1.3. Correlated Assets 2.1.4. Portfolio Separation and the Market Portfolio 2.2. Capital Market Theory, Part I 2.2.1. Linear Algebraic Approach 2.2.2. Efficient Mean-Standard Deviation Frontier 2.3. Capital Market Theory, Part II 2.3.1. Capital Market Line 2.3.2. CAPM Formula; Asset β 2.3.3. Systematic and Non-Systematic Risk; Pricing Using CAPM 2.4. Utility Theory 2.4.1. Securities and Axioms for Investor Behavior 2.4.2. Indifference Curves, Certainty Equivalent, Risk Aversion 2.4.3. Examples of Utility Functions 2.4.4. Absolute and Relative Risk Aversion 2.4.5. Utility Maximization 2.5. Multiple Period Portfolio Problems 2.5.1. Problem Description and Dynamic Programming Approach 2.5.2. Examples 2.5.3. Optimal Portfolios and Martingales Chapter 3 - Derivatives Valuation in Multiple Periods 3.1. Options Pricing for Multiple Time Periods 3.1.1. Introduction 3.1.2. Valuation by Chaining 3.1.3. Valuation by Martingales 3.2. Key Ideas of Discrete Probability, Part I 3.2.1. Algebras and Measurability 3.2.2. Independence 3.3. Key Ideas of Discrete Probability, Part II 3.3.1. Conditional Expectation 3.3.2. Application to Pricing Models 3.4. Fundamental Theorems of Options Pricing 3.4.1. The Market Model 3.4.2. Gain, Arbitrage, and Attainability 3.4.3. Martingale Measures and the Fundamental Theorems 3.5. Valuation of Non-Vanilla Options 3.5.1. American and Bermudan Options 3.5.2. Barrier Options 3.5.3. Asian Options 3.5.4. Two-Asset Options 3.6. Derivatives Pricing by Simulation 3.6.1. Setup and Algorithm 3.6.2. Examples 3.7. From Discrete to Continuous-Time (A Preview) Chapter 4 - Continuous Probability Models 4.1. Continuous Distributions and Expectation 4.1.1. Densities and Cumulative Distribution Functions 4.1.2. Expectation 4.1.3. Normal and Lognormal Distributions 4.2. Joint Distributions 4.2.1 Basic Ideas 4.2.2. Marginal and Conditional Distributions 4.2.3. Independence 4.2.4. Covariance and Correlation 4, 2, 5 Bivariate Normal Distribution 4.3. Measurability and Conditional Expectation 4.3.1. Sigma Algebras 4.3.2. Random Variables and Measurability 4.3.3. Continuous Conditional Expectation 4.4. Brownian Motion and Geometric Brownian Motion 4.4.1. Random Walk Processes 4.4.2. Standard Brownian Motion 4.4.3. Non-standard Brownian motion 4.4.4. Geometric Brownian Motion 4.4.5. Brownian Motion and Binomial Branch Processes 4.5. Introduction to Stochastic Differential Equations 4.5.1. Meaning of the General SDE 4.5.2. Ito's Formula 4.5.3. Geometric Brownian Motion as Solution Chapter 5 - Derivative Valuation in Continuous Time 5.1. Black-Scholes Via Limits 5.1.1. Black-Scholes Formula 5.1.2. Limiting Approach 5.1.3. Put Options and Put-Call Parity 5.2. Black-Scholes via Martingales 5.2.2. Fundamental Theorems of Asset Pricing 5.2.2. Trading Strategies and Martingale Valuation 5.2.3. Martingale Measures 5.2.4. Asset and Bond Binaries 5.2.5. Other Binary Derivatives 5.3. Black-Scholes via Differential Equations 5.3.1. Deriving the PDE 5.3.2. Boundary Conditions; Solving the PDE 5.4. Checking Black-Scholes Assumptions 5.4.1. Normality of Rates of Return 5.4.2. Stability of Parameters 5.4.3. Independence of Rates of Return Appendices A. Multivariate Normal Distribution A.1 Review of Matrix Concepts A, 2.Multivariate Normal Distribution B. Answers to Selected Exercises
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2022
• Extent: 1 online resource
• Subjects: 332.0151; Business mathematics
• Languages: English
• ISBNs: 9781498780445; 9781498780421
• Related ISBNs: 9781498780407
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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