programme

Mathematical Finance

Home/ Mathematical Finance
Course TypeCourse CodeNo. Of Credits
Foundation ElectiveSUS1MA5364

Semester and Year Offered: Monsoon Semester 2013-14

Course Coordinator and Team: Balchand Prajapati

Email of course coordinator: balchand@aud.ac.in

Pre-requisites: Pre-requisite for this course is Mathematics at the XII grade level.

Aim: The main motive of this course is to give students a basic introduction to finance and the applications of mathematics to it. In the digital era with algorithmic trading and mathematical modelling being used to understand stock market behaviour and understand large dynamic data, this introductory course in Mathematical finance is well placed to prepare students interested in understanding and choosing a career in the world of mathematical finance.

Course Outcomes:

After completing this course, students will be able

  1. to have Basic Concepts of Mathematical Finance
  2. Deterministic Cash Flows, Random Cash Flows
  3. Forwards and Futures, Stock Price Models, Options
  4. The Black-Scholes Model

Brief description of modules/ Main modules:

The following topics will be covered in the course under the four main modules as described below.

  • Basic Concepts of Mathematical Finance Arbitrage, Return and Interest, Time value of money, Bonds, shares and indices
  • Deterministic Cash Flows Net Present Value, Internal rate of return, A comparison of IRR and NPV, Bonds: price and yield, Clean and dirty price, Price-yield curves, Duration, Term structures of interest rates, Immunization, Convexity
  • Random Cash Flows Random returns, Portfolio diagrams and efficiency, Feasible set, Markowitz model, Capital Asset Pricing Model, Diversification, APM as a pricing formula, Numerical techniques, Lagrange Multipliers
  • Forwards and Futures Forwards and futures, Forward and futures price, Value of futures contract, Method of replicating portfolios, Hedging with futures, Currency futures, Stock index futures
  • Stock Price Models Lognormal model, Geometric Brownian motion, Suitability of GBM for stock prices, Binomial tree model
  • Options Call options, Put options, Put-call parity, Binomial options pricing model, Pricing American options, Factors influencing option premiums, Options for assets with dividends, Dynamic hedging, Risk-neutral valuation
  • The Black-Scholes Model Risk-neutral valuation, The Black-Scholes Formula, Implied Volatility, Dynamic Hedging, The Greeks
  • Lab Exercises
  1. Selections from Interest and Amortization, Cash Flow Analysis, Sharpe Index, Jensen’s Alpha.
  2. Selections from Optimal Hedge Ratio, 2 and 3-asset BOPM, Dynamic Hedging, Factors Influencing Options Prices, Implied versus Historical Volatility.

Assessment Details with weights:

S.No

Assessment

Date/period in which Assessment will take place

Weightage

1

Class test

First week of February

10%

2

Mid Semester Exam

As per AUD Academic Calendar

25%

3

Home assignment/Tut

Throughout the semester

15%

4

Presentation/ Viva

May

15%

5

End Semester Exam

As per AUD Academic Calendar

35%

 

Reading List:

  • Martin Anthony and Norman Biggs, Mathematics for economics and finance, Methods and Modelling, Cambridge University Press, 2012.
  • M Capinski and T Zastawniak, Mathematics for Finance, Springer (International Edition), 2003.
  • Amber Habib, The Calculus of Finance, Universities Press, 2011.
  • David Luenberger, Investment Science, Oxford University Press (Indian Edition), 1997.
  • Sheldon Ross, An Elementary Introduction to Mathematical Finance (2nd edition), Cambridge University Press (Indian Edition), 2005.