Introduction to Mathematical Finance | Department of Mathematics

# Introduction to Mathematical Finance

A Major Elective for B.Sc. (Research) Mathematics. Cross-listed as FAC201.

Credits (Lec:Tut:Lab): 3:0:1 (3 lectures and 1 two-hour lab weekly)

Prerequisites: MAT 184 Probability or MAT 205 Mathematical Methods III or CSD209.

Overview: Mathematical Finance is a modern study area where mathematical methods are used to create and add immense value in a practical environment. The aim of this course is twofold. First, to discuss the mathematical models that have driven the explosion of financial services and products over the last 30 years or so. Second, to use spreadsheet programs to work with actual data. This course is also the gateway to our Specialization in Mathematical Finance.

Detailed Syllabus:

1. Basic concepts: Bonds and shares, risk versus profit, return and interest, time value of money, arbitrage.
2. Fixed Income Securities: Net Present Value and Internal Rate of Return, price and yield of a bond, term structures, duration, immunization.
3. Mean-Variance Analysis: Random returns, efficient portfolios, feasible set, Markowitz model, Two Fund and One Fund Theorems, Capital Asset Pricing Model and applications.
4. Forwards, Futures and Swaps: Replicating portfolios, futures on assets without income, futures on assets with fixed income or dividend yield, hedging with futures, currency futures, stock index futures, forward rate agreements, interest rate swaps, currency swaps, equity swaps.
5. Stock Price Models: Geometric Brownian Motion, Binomial Tree.
6. Options: Call and put options, put-call parity, Binomial Options Pricing Model, dynamic hedging, risk-neutral valuation, Black-Scholes formula, trading strategies.
7. Labs: Microsoft Excel and VBA.

References:

1. Principles of Finance with Excel 2nd edition by Simon Benninga, Oxford University Press, 2010.
2. Mathematics for Finance by M Capinski and T Zastawniak, Springer (International Edition), 2003.
3. The Calculus of Finance by Amber Habib, Universities Press, 2011.
4. Options, Futures and Other Derivatives 7th edition by John C Hull and Sankarshan Basu, Pearson 2009.
5. Investment Science by David Luenberger, Oxford University Press (Indian Edition), 1997.
6. An Elementary Introduction to Mathematical Finance 2nd edition by Sheldon Ross, Cambridge University Press (Indian Edition), 2005.

Past Instructors: Amber Habib, Charu Sharma, Sunil Bowry

Course Code:
MAT390
Course Credits:
4.00
Department:
Course Level: