Course info

Course Objective: 

This course introduces the basic mathematics to be used in finance. It is ideal for the students who want to a rigorous study in finance in their final year of under-graduation level. This course ensures that students can experience mathematical and economic perspective of the subject. Using mathematics as a tool this course covers a wide range of topics in finance, such as, the time value of money, portfolio theory, capital market theory, security price modeling, and financial derivatives.

Course Outcomes:  The students will be able to

1

Understand the mathematical foundation of quantitative finance

2

Grasp the standard and advanced quantitative methodologies applied in the area of financial economics.

3

Create and evaluate the potential models for the pricing of shares and bonds.

4

Construct, analyze and evaluate the models for investment of financial assets.

5

Understand the emerging theories and techniques in the area of financial economics.

Course Content:  

 UNIT I

Review of basic mathematical tools, probability theory and random variables. Economic indicators that may affect the financial markets. Mathematics of the Time Value of Money: Simple interest, Compound interest, Annuities and amortization theory, NPV, IRR.

10 hrs

 UNIT II

Mathematics of Investment: Buying and selling stocks, Common stock valuation, cost of new issues of common stock, stock value with two-stage dividend growth, Bond valuation, premium and discount prices, premium amortization, discount accumulation,

10 hrs

UNIT III

Estimating the yield rate.  Mathematics of Return and Risk: Expected rate of return, measuring the risk, risk aversion and risk premium, return and risk at the portfolio level.

10 hrs

 UNIT IV

Portfolio Theory I: Markowitz Portfolio Model, Two securities portfolio, N-securities portfolio, Investor Utility, Diversification and randomly selected securities. Capital market Theory: the financial beta (β),

10 hrs

UNIT V

Portfolio Theory II: The Capital Market line, The CAPM equation, The Security Market Line, CAPM security risk decomposition. Portfolio Risk Measures: The Sharpe ratio, the Sortino ration, Value-at-Risk.

10 hrs

UNIT VI

Derivatives: Forwards, Futures and Options. Dynamics of making profits with options, Intrinsic Values of Calls and Puts, Time value of Calls and Puts, The delta ratio, determinates of option value, Option valuation. Option Pricing: The Black-Scholes-Merton (BSM) mode. The BSM model vs market data.

10 hrs

Internal Assessment: 

 CIA 1

Unit I, Unit II 

 CIA 2

Assignment submission and/or presentation 

Text Books: 

1.       A. O. Petters and X. Dong, An Introduction to Mathematical Finance with Applications (Springer, 2016)

2.       M. J. Alhabeeb, Mathematical Finance, (Wiley, 2012)

 Reference Books: 

3.       S. Ross, An Elementary Introduction to Mathematical Finance, Third Edition (Cambrige U. Press, Cambridge, 2011)

4.       J Janssen, R. Manca, and E. V. di Prignano, Mathematical Finance: Deterministic and Stochastic Models (Wiley, 2009)

S. Roman, Introduction to the Mathematics of Finance (Springer, 2004)