Mathematics for Finance An Introduction to Financial Engineering 1st edition by Marek Capinski, Tomasz Zastawniak – Ebook PDF Instant Download/Delivery: 1852333308, 9781852333300
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ISBN 10: 1852333308
ISBN 13: 9781852333300
Author: Marek Capinski, Tomasz Zastawniak
Designed to form the basis of an undergraduate course in mathematical finance, this book builds on mathematical models of bond and stock prices and covers three major areas of mathematical finance that all have an enormous impact on the way modern financial markets operate, namely: Black-Scholesâ arbitrage pricing of options and other derivative securities; Markowitz portfolio optimization theory and the Capital Asset Pricing Model; and interest rates and their term structure. Assuming only a basic knowledge of probability and calculus, it covers the material in a mathematically rigorous and complete way at a level accessible to second or third year undergraduate students. The text is interspersed with a multitude of worked examples and exercises, so it is ideal for self-study and suitable not only for students of mathematics, but also students of business management, finance and economics, and anyone with an interest in finance who needs to understand the underlying theory.
Mathematics for Finance An Introduction to Financial Engineering 1st Table of contents:
Chapter 1: Introduction to Market Models
1.1 Fundamental Concepts and Assumptions
1.2 Principle of No-Arbitrage
1.3 Binomial Model (One-Step)
1.4 Assessing Risk and Return
1.5 Forward Contracts
1.6 Call and Put Options
1.7 Risk Management through Options
Chapter 2: Risk-Free Assets
2.1 Time Value of Money
2.1.1 Simple Interest
2.1.2 Compounding (Periodic)
2.1.3 Payment Streams
2.1.4 Continuous Compounding
2.1.5 Comparison of Compounding Methods
2.2 Money Market Instruments
2.2.1 Zero-Coupon Bonds
2.2.2 Coupon Bonds
2.2.3 Money Market Account
Chapter 3: Risky Assets
3.1 Stock Price Dynamics
3.1.1 Return Calculation
3.1.2 Expected Return
3.2 Binomial Tree Model
3.2.1 Risk-Neutral Probabilities
3.2.2 Martingale Property
3.3 Alternative Models
3.3.1 Trinomial Tree Model
3.3.2 Continuous-Time Limit
Chapter 4: Discrete Time Market Models
4.1 Stock and Money Market Models
4.1.1 Investment Strategies
4.1.2 No Arbitrage Principle
4.1.3 Application in Binomial Models
4.1.4 Fundamental Asset Pricing Theorem
4.2 Extended Market Models
Chapter 5: Portfolio Management
5.1 Understanding Risk
5.2 Portfolios of Two Securities
5.2.1 Risk and Expected Return on Portfolios
5.3 Portfolios with Multiple Securities
5.3.1 Portfolio Risk and Expected Return
5.3.2 Efficient Frontier
5.4 Capital Asset Pricing Model (CAPM)
5.4.1 Capital Market Line
5.4.2 Beta Coefficient
5.4.3 Security Market Line
Chapter 6: Forward and Futures Contracts
6.1 Forward Contracts
6.1.1 Forward Pricing
6.1.2 Value of Forward Contracts
6.2 Futures Contracts
6.2.1 Pricing Mechanisms
6.2.2 Hedging with Futures
Chapter 7: General Properties of Options
7.1 Definitions
7.2 Put-Call Parity
7.3 Option Pricing Limits
7.3.1 European Options
7.3.2 Non-Dividend Stock Options
7.3.3 American Options
7.4 Option Price Determinants
7.4.1 European Options
7.4.2 American Options
7.5 Time Value of Options
Chapter 8: Option Pricing Techniques
8.1 European Options (Binomial Tree Model)
8.1.1 Single-Step Model
8.1.2 Two-Step Model
8.1.3 Multi-Step Model
8.1.4 Cox–Ross–Rubinstein Formula
8.2 American Options in Binomial Models
8.3 Black–Scholes Formula
Chapter 9: Financial Engineering
9.1 Hedging Options
9.1.1 Delta Hedging
9.1.2 Greek Parameters
9.1.3 Practical Applications
9.2 Hedging Business Risks
9.2.1 Value at Risk
9.2.2 Case Study
9.3 Speculation with Derivatives
9.3.1 Speculative Tools
9.3.2 Case Study
Chapter 10: Variable Interest Rates
10.1 Maturity-Independent Yields
10.1.1 Single Bond Investments
10.1.2 Duration
10.1.3 Bond Portfolios
10.1.4 Dynamic Hedging
10.2 Term Structure Models
10.2.1 Forward Rates
10.2.2 Money Market Accounts
Chapter 11: Stochastic Interest Rates
11.1 Binomial Model Applications
11.2 Arbitrage Bond Pricing
11.2.1 Risk-Neutral Probabilities
11.3 Interest Rate Derivatives
11.3.1 Options
11.3.2 Swaps
11.3.3 Caps and Floors
11.4 Final Remarks
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