Financial Mathematics A Comprehensive Treatment 1st Edition by Giuseppe Campolieti, Roman N Makarov – Ebook PDF Instant Download/Delivery: 9780429994579
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ISBN 13: 9780429994579
Author: Giuseppe Campolieti, Roman N Makarov
The book has been tested and refined through years of classroom teaching experience. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. This textbook provides complete coverage of discrete-time financial models that form the cornerstones of financial derivative pricing theory. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. Key features: In-depth coverage of discrete-time theory and methodology. Numerous, fully worked out examples and exercises in every chapter. Mathematically rigorous and consistent yet bridging various basic and more advanced concepts. Judicious balance of financial theory, mathematical, and computational methods. Guide to Material. This revision contains: Almost 200 pages worth of new material in all chapters. A new chapter on elementary probability theory. An expanded the set of solved problems and additional exercises. Answers to all exercises. This book is a comprehensive, self-contained, and unified treatment of the main theory and application of mathematical methods behind modern-day financial mathematics.
Financial Mathematics A Comprehensive Treatment 1st Table of contents:
1 Mathematics of Compounding
1.1 Interest and Return
1.1.1 Amount Function and Return
1.1.2 Simple Interest
1.1.3 Periodic Compound Interest
1.1.4 Continuous Compound Interest
1.1.5 Equivalent Rates
1.1.6 Continuously Varying Interest Rates
1.2 Time Value of Money and Cash Flows
1.2.1 Equations of Value
1.2.2 Deterministic Cash Flows and Their Net Present Values
1.3 Annuities
1.3.1 Simple Annuities
1.3.2 Determining the Term of an Annuity
1.3.3 General Annuities
1.3.4 Perpetuities
1.3.5 Continuous Annuities
1.4 Bonds
1.4.1 Introduction and Terminology
1.4.2 Zero-Coupon Bonds
1.4.3 Coupon Bonds
1.4.4 Serial Bonds, Strip Bonds, and Callable Bonds
1.5 Yield Rates
1.5.1 Internal Rate of Return and Evaluation Criteria
1.5.2 Determining Yield Rates for Bonds
1.5.3 Approximation Methods
1.5.4 The Yield Curve
1.6 Yield Risk and Duration
1.6.1 Immunization
1.7 Exercises
2 Primer on Pricing Risky Securities
2.1 Stocks and Stock Price Models
2.1.1 Underlying Assets and Derivative Securities
2.1.2 Basic Assumptions for Asset Price Models
2.2 Basic Price Models
2.2.1 A Single-Period Binomial Model
2.2.2 A Discrete-Time Model with a Finite Number of States
2.2.3 Introducing the Binomial Tree Model
2.2.4 Recursive Construction of a Binomial Tree
2.2.5 Self-Financing Investment Strategies in the Binomial Model
2.2.6 Log-Normal Pricing Model
2.3 Arbitrage and Risk-Neutral Pricing
2.3.1 The Law of One Price
2.3.2 A First Look at Arbitrage in the Single-Period Binomial Model
2.3.3 Arbitrage in the Binomial Tree Model
2.3.4 Risk-Neutral Probabilities
2.3.5 Martingale Property
2.3.6 Risk-Neutral Log-Normal Model
2.4 Value at Risk
2.5 Dividend Paying Stock
2.6 Exercises
3 Portfolio Management
3.1 Expected Utility Functions
3.1.1 Utility Functions
3.1.2 Mean-Variance Criterion
3.2 Portfolio Optimization for Two Assets
3.2.1 Portfolio of Two Risky Assets
3.2.2 Portfolio Lines
3.2.3 The Minimum Variance Portfolio
3.2.4 Selection of Optimal Portfolios
3.3 Portfolio Optimization for N Assets
3.3.1 Portfolios of Several Assets
3.3.2 The Minimum Variance Portfolio
3.3.3 Minimum Variance Portfolio Line
3.3.4 Case without Short Selling
3.3.5 Maximum Expected Utility Portfolio
3.3.6 Efficient Frontier and Capital Market Line
3.4 The Capital Asset Pricing Model
3.5 Exercises
4 Primer on Derivative Securities
4.1 Forward Contracts
4.1.1 No-Arbitrage Evaluation of Forward Contracts
4.1.2 Value of a Forward Contract
4.2 Basic Options Theory
4.2.1 Payoffs of Standard Options
4.2.2 Put-Call Parities
4.2.3 Properties of European Options
4.2.4 Early Exercise and American Options
4.2.5 Nonstandard European-Style Options
4.3 Fundamentals of Option Pricing
4.3.1 Pricing of European-Style Derivatives in the Binomial Tree Model
4.3.2 Pricing of American Options in the Binomial Tree Model
4.3.3 Option Pricing in the Log-Normal Model: The Black–Scholes–Merton Formula
4.3.4 Greeks and Hedging of Options
4.3.5 Black–Scholes Equation
4.4 Exercises
II Discrete-Time Modelling
5 Single-Period Arrow–Debreu Models
5.1 Specification of the Model
5.1.1 Finite-State Economy. Vector Space of Payoffs. Securities
5.1.2 Initial Price Vector and Payoff Matrix
5.1.3 Portfolios of Base Securities
5.2 Analysis of the Arrow–Debreu Model
5.2.1 Redundant Assets and Attainable Securities
5.2.2 Completeness of the Model
5.3 No-Arbitrage Asset Pricing
5.3.1 The Law of One Price
5.3.2 Arbitrage
5.3.3 The First Fundamental Theorem of Asset Pricing
5.3.4 Risk-Neutral Probabilities
5.3.5 The Second Fundamental Theorem of Asset Pricing
5.3.6 Investment Portfolio Optimization
5.4 Pricing in an Incomplete Market
5.4.1 A Trinomial Model of an Incomplete Market
5.4.2 Pricing Unattainable Payoffs: The Bid-Ask Spread
5.5 Change of Numéraire
5.5.1 The Concept of a Numéraire Asset
5.5.2 Change of Numéraire in a Binomial Model
5.5.3 Change of Numéraire in a General Single Period Model
5.6 Exercises
6 Introduction to Discrete-Time Stochastic Calculus
6.1 A Multi-Period Binomial Probability Model
6.1.1 The Binomial Probability Space
6.1.2 Random Processes
6.2 Information Flow
6.2.1 Partitions and Their Refinements
6.2.2 Sigma-Algebras
6.2.3 Filtration
6.2.4 Filtered Probability Space
6.3 Conditional Expectation and Martingales
6.3.1 Measurability of Random Variables and Processes
6.3.2 Conditional Expectations
6.3.3 Properties of Conditional Expectations
6.3.4 Conditioning in the Binomial Model
6.3.5 Binomial Model with Interdependent Market Moves
6.3.6 Sub-, Super-, and True Martingales
6.3.7 Classification of Stochastic Processes
6.3.8 Stopping Times
6.4 Exercises
7 Replication and Pricing in the Binomial Tree Model
7.1 The Standard Binomial Tree Model
7.2 Self-Financing Strategies and Their Value Processes
7.2.1 Equivalent Martingale Measures for the Binomial Model
7.3 Dynamic Replication in the Binomial Tree Model
7.3.1 Dynamic Replication of Payoffs
7.3.2 Replication and Valuation of Random Cash Flows
7.4 Pricing and Hedging Non-Path-Dependent Derivatives
7.5 Pricing Formulae for Standard European Options
7.6 Pricing and Hedging Path-Dependent Derivatives
7.6.1 Average Asset Prices and Asian Options: Recursive Evaluation
7.6.2 Extreme Asset Prices and Lookback Options
7.6.3 Recursive Evaluation of Lookback Options
7.7 American Options
7.7.1 Writer’s Perspective: Pricing and Hedging
7.7.2 Buyer’s Perspective: Optimal Exercise
7.7.3 Early-Exercise Boundary for Non-Path-Dependent Options
7.7.4 Pricing American Options: The Case with Dividends
7.8 Exercises
8 General Multi-Asset Multi-Period Model
8.1 Main Elements of the Model
8.2 Assets, Portfolios, and Strategies
8.2.1 Payoffs and Assets
8.2.2 Static and Dynamic Portfolios
8.2.3 Self-Financing Strategies
8.2.4 Replication of Payoffs
8.3 Fundamental Theorems of Asset Pricing
8.3.1 Arbitrage Strategies
8.3.2 Enhancing the Law of One Price
8.3.3 Equivalent Martingale Measures
8.3.4 Calculation of Martingale Measures
8.3.5 The First and Second FTAP
8.3.6 Pricing and Hedging Derivatives
8.3.7 Pricing under the Markov Property
8.3.8 Radon–Nikodym Derivative Process and Change of Numéraire
8.4 More Examples of Discrete-Time Models
8.4.1 Binomial Tree Model with Stochastic Volatility
8.4.2 Binomial Tree Model for Interest Rates
8.4.3 Interest Rates with the Markov Property
8.4.4 Forward Measures for Interest-Rate Derivative Pricing
8.5 Exercises
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Tags: Giuseppe Campolieti, Roman N Makarov, Financial, Mathematics