Financial engineering. Methods and cases

This textbook contains materials for several courses which are taught in the Master’s Programme in Financial Engineering that is run at the Poznań University of Economics and Business. The book consists of seven chapters that cover the main areas of quantitative finance: investment, financial instruments pricing, financial risk measuring and management as well as corporate finance. The main part of the book is devoted to the mathematical models used in the field of finance. There are four chapters devoted to the pricing of financial instruments: from pricing equities using Capital Asset Pricing Model, through derivative instruments on equites, to more complicated derivatives on interest rates. The last topic is illustrated with some genuine examples from the markets in the post-crisis period. One chapter describes basic models and concepts used in measuring financial risk. Two other chapters are about investment. One describes the way in which companies finance their activities. The second one describes investment strategies of hedge funds. All chapters contain exercises and examples from the real markets.In order to understand the topics from the textbook, some prerequisites are required. It is assumed that a potential reader knows the basics of probability theory, linear algebra and calculus. The knowledge of econometrics and statistical methods used in economics will also be useful in better comprehension of the book. All these issues are usually taught in Bachelor’s programmes in Economics or Finance.

Preface
Chapter
Multifactor models: Portfolio theory
1.1. Capital asset pricing model
1.2. The characteristic line–market model
1.2.1. Model specification
1.2.2. Examples of the market model estimation
1.2.3. Stability of beta
1.2.4. Market portfolio: The most important indices
1.3. Multifactor models 23
1.3.1. Fama and French (1992)
1.3.2. Momentum and further extensions
1.3.3. Liquidity premium
Further readings
Chapter 2
Financial risk measurement
2.1. Financial risk management
2.2. Market risk measurement
2.2.1. Value at risk methods
2.2.1.1. Historical simulation method (HS)
2.2.1.2. Variance-covariance method (VC)
2.2.1.3. Monte Carlo methods (MC)
2.2.2. Backtesting
2.3. Credit risk
2.3.1. Credit ratings
2.3.2. Internal credit ratings
2.3.3. Measuring default risk probabilities from bond spreads
2.3.4. Measuring default risk probabilities from equity prices
Further readings
Chapter 3
Introduction to derivative instruments pricing
3.1. Pricing in one-period model
3.1.1. Stochastic model of market
3.1.2. Arbitrage opportunity and the First Fundamental Theorem of Asset Pricing
3.1.3. Replication and completeness of the market
3.1.4. Martingale pricing
3.1.5. Second Fundamental Theorem of Asset Pricing
3.2. Pricing in multi-period models
3.2.1. Multi-period stochastic model of market
3.2.2. No-arbitrage and martingale measures
3.2.3. Replication and market completeness
Further readings
Chapter 4
Corporate financing–designing and offering securities
4.1. Designing securities
4.1.1. Control rights versus cash flow rights
4.1.2. One share–one vote principle and control-enhancing mechanisms
4.1.3. Seniority and security in corporate debt instruments
4.2. Aims of security offerings
4.3. Side effects of stock offerings: Dilution and wealth transfers
4.4. Security offerings and companies’ life cycle
4.5. Types of offerings
4.5.1. Private placements
4.5.2. Initial public offerings
4.5.2.1. Basics of IPOs and reasons for going public
4.5.2.2. IPO procedures and requirements
4.5.2.3. The role of investment banks in IPO
4.5.3. Secondary (seasoned) public offerings
4.5.4. Rights offerings (issues)
Further readings
Chapter 5
Modeling a term structure of interest rates
5.1. Interest rates and bonds
5.1.1. Compounding and discounting
5.1.2. Discount factors
5.1.3. Forward rates
5.2. Estimating term structure of interest rates
5.2.1. Data for estimation
5.2.1.1. Interbank market interest rates
5.2.1.2. Bonds
5.2.2. Bootstrapping
5.2.3. Spline method
5.2.4. Nelson-Siegel model
5.2.5. Svensson model
5.2.6. Estimation of a term structure by central banks
Further readings
Chapter 6
Yield curves construction methods: Key concepts and evolution of market practice
6.1. Introduction
6.2. Key definitions
6.2.1. Key notations
6.2.2. Day count conventions
6.2.3. Interest rate derivatives
6.2.3.1. FRA
6.2.3.2. IRS
6.2.3.3. TBS
6.2.3.4. OIS
6.2.4. Cross-currency trades
6.2.4.1. FX swap
6.2.4.2. CIRS
6.3. Zero-coupon and discount curves construction
6.3.1. Bootstrapping the money market rates
6.3.2. Interpolation
6.3.2.1. Simple interpolation methods
6.3.2.2. Cubic splines
6.4. Bootstrapping of zero curves in the multi-curve framework
6.4.1. What has changed and why?
6.4.2. Building the discount curve
6.4.3. Building the forward curve
6.5. Summary
Further readings
Chapter 7
Hedge fund strategies
Introduction
7.1. Definition and attributes of hedge funds
7.1.1. Active management and absolute returns
7.1.2. Flexible investment policy
7.1.3. Unusual legal structure
7.1.4. Developed structure of fees
7.1.5. Manager as a partner, not an employee
7.1.6. Offered to specific investors
7.1.7. Limited capacity
7.1.8. Limited liquidity
7.1.9. Limited transparency
7.2. Types and characteristics of hedge fund strategies
7.2.1. Directional strategies
7.2.2. Non-directional or relative value strategies
7.2.3. Event driven funds
7.2.4. Hybrid and other funds