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Regular version of the site
Master 2019/2020

## Economic and Mathematic Modeling

Type: Compulsory course (Big Data Systems)
Delivered by: Department of Information Systems and Digital Infrastructure Management
When: 1 year, 1 module
Mode of studies: offline
Master’s programme: Big Data Systems
Language: English
ECTS credits: 3

### Course Syllabus

#### Abstract

"Economic and Mathematical Modeling" is taken in the first module of the Master’s program “Big Data Systems”. This is a crash course on a mix of quantitative finance, investment management and corporate finance reviewing major quantitative methods used in finance. It covers the traditional topics such as percentage calculus, making capital budget decisions, fixed-income securities, stock valuation, portfolio management including the CAPM and APT models and financial derivatives. While providing the basic insight into each topic, we also focus on the subtleties which are usually omitted in the standard expositions to quantitative methods. For example, we discuss the use of the standard measures like IRR for mutually exclusive projects in capital budgeting, term structure of interest rates in bond valuation, the APT model, to name a few. The framework of the course is the no-arbitrage argument which is repeatedly exploited to demonstrate the pricing for an asset. The duration of the course is one module. The course is taught in English and worth 3 credits.

#### Learning Objectives

• The course provides a review of major methods of quantitative finance

#### Expected Learning Outcomes

• Be able to use the concepts of time value of money
• Be able to compute basic indicators of investments including NPV, IRR etc
• Understand the desing and principles of fixed income instruments. Be able to calculate the basic indicators asssociated with bonds
• Be able to evaluate the stocks by means of the discount dividend models.
• Understand the principles of asset allocation. Be able to evaluate the risk and return of the portfolio of assets.
• Understand the principles of financila derivatives/ Be able to calculate the price for options and futures

#### Course Contents

• Percentage calculus, time value of money
Time value of money: future value and different schemes of compounding, perpetuities, annuities, effective annual rates. Present value and discounting. Cash flows. Structure of the cash flows. Effective annual costs and replacement decisions.
• Making capital budget decisions
Investment rules: NPV, IRR, payback, discounted payback, PI. Non-standard situations (mutually exclusive projects, scale, problem, timing, etc). Incremental cash flows. Inflation and capital budgeting. Profitability of trading on margin and short sales.
• Fixed income securities
Bond features and prices. Yield to maturity. Bond prices over time. Term structure of interest rates. Holding period returns, spot, short and future rates. Theories and implications of the term structure. Duration of a bond. Immunization against deviations of the interest rates. Managing bond portfolios.
• Stock valuation
Intrinsic value versus market price. Dividend discount models. The constant-growth DDM. Convergence of price to intrinsic value. Multistage growth models. Price-earnings ratio and its determinants. Free cash flow valuation.
• Portfolio management
Portfolios of two risky assets. The Markowitz portfolio optimization model: security selection, capital allocation and the separation property. The power of diversification. The capital asset pricing model: expected returns on Individual securities, the security market line. The CAPM and the single-index market. Assumptions and extensions of the CAPM. The arbitrage pricing theory.
• Mathematics of derivatives
Futures and options trading. American and European options. Values of options at expiration. Call and put options. Option versus stock. Option strategies: protective put, covered call, straddle, spreads, collars etc. The put-call parity. Option valuation: intrinsic and time values. Determinants of option prices. Binomial option pricing. Stochastic calculus (Ito’s lemma etc). Security price as a random walk. Black-Scholes option valuation. The Black-Scholes formula. Impact of dividends.

#### Assessment Elements

• in-class tests
• Final Exam

#### Interim Assessment

• Interim assessment (1 module)
0.4 * Final Exam + 0.6 * in-class tests

#### Recommended Core Bibliography

• Dempsey, M. (2020). Investment Analysis : An Introduction to Portfolio Theory and Management. London: Routledge. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2278900
• Hull, J. C. (2017). Options, Futures, and Other Derivatives, Global Edition. [Place of publication not identified]: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1538007