Lahore University of Management Sciences

MATH 452 – Mathematics for Finance Fall 2012-2013

Instructor Adnan Khan/Mudassar Imran

Room No. TBA

Office Hours TBA

Email adnan.khan@lums.edu.pk / mudasar.imran@lums.edu.pk

Telephone 8015 / 8284

Secretary/TA TBA

TA Office Hours TBA

Course URL (if any) http://suraj.lums.edu.pk/~adnan.khan/classes/classes/MathFinance

Course Basics

Credit Hours 4

Lecture(s) Nbr of Lec(s) Per Week 2 Duration 110 min

Course Distribution

Core

Elective

Open for Student Category Juniors/Seniors

Close for Student Category None

COURSE DESCRIPTION

This course is a standalone introduction to mathematical techniques in quantitative finance (QF) or a complementary course stressing the mathematics involved in QF for finance students. Both discrete and continuous time models for pricing of bonds, stocks and derivative financial instruments will be presented. The major results discussed include the Binomial Tree Model, the Markowitz Portfolio Optimization theory, the Capital asset pricing model and the Black Scholes Model.

COURSE Anti-PREREQUISITE(S)

Calculus I & II, Linear Algebra, Differential Equations, Probability OR Consent of the Instructor

COURSE OBJECTIVES

Be familiar with some widely used financial instruments Understand how these instruments are priced Understand how these instruments are used to hedge risk

Learning Outcomes

Students will learn : How to calculate the time value of money What are bonds, forwards, futures and options, and how to calculate their price What is a Weiner process and how is it used to model stock prices Ito stochastic calculus and its use in finance Modern Portfolio Theory How to hedge risk using these financial instruments

Grading Breakup and Policy

Assignment(s): 30% Midterm Examination: 25% Final Examination: 25% Project: 20%

Lahore University of Management Sciences

Lecture Topics Recommended

Readings

1 Introduction to Discrete Time Market Models

2 Probability on Discrete Spaces, Random Variables, Distributions

3 Expectation, Conditioning, Martingale and Markov Properties

4 Time Value of Money, Compounding Methods, Annuities & Perpetuities

5 Money Market, Bonds

6 Dynamics of Stock Prices: Binomial Model, Risk Neutral Probability

7 Market Models: Investment Strategies, Fundamental Theorem of Asset Pricing

8 Portfolio Management: Risk, Expected Return and Efficient Frontier

9 Capital Asset Pricing Model

10 Forwards and Futures Contracts

11 Introduction, Vanilla Options

12 Variables determining option prices

13 Option Pricing using Binomial Model, CRR Formula, American Options

14 Hedging Option Positions and Risk

15 Probability on Continuous Spaces, Random Variables

16 Expectation, Conditioning, Martingale and Markov Properties

17 Random Walks, Martingale Property, Scaling, Continuous Limit

18 Brownian Motion, Quadratic Variation, Markov Property and Martingale Properties

19 Ito’s Lemma , Ito Integral, Construction and Properties

20 Black Scholes (BS) Equation, Derivation and Variants

21 Solving the BS Equation: European Puts and Calls

22 Value of Portfolio and Pricing under Risk Neutral Measure

23 Fundamental Theorem of Asset Pricing

24 Forwards and Futures

25 Stopping Times, Perpetual American Put, Finite Expiration American Put

26 Finite Difference Methods for Solving the BS Equation Numerically

27 Solving the BS Equation using Finite Differences

28 Monte Carlo Methods: Plain Vanillas

Textbook(s)/Supplementary Readings

Required Text(s): Capinski. M & Zastawniak. T, Mathematics for Finance, Springer 2003 Higham. D, An Introduction to Financial Option Valuation, Cambridge University Press 2004 Reference(s): Wilmott. P, Paul Wilmott on Quantitative Finance, Wiley 2006 Shreve. S.E, Stochastic Calculus for Finance I & II, Springer 2000