Quantitative Finance

FINN 422/MATH449/MATH524

Spring 25

 

 

Instructor: Adnan Khan [(adnan.khan@lums.edu.pk), Office Hours: R 11:30 - 1:30 SSE 149], Riaz Ahmad [(r.ahmad@ucl.ac.uk) Office Hours: M W 9-12]

Co-Instructor / TA: Ayesha Ahmed [Simulation Lab]

Class Logistics

Lecture: M-W, 12:00-1:15 am – 9-B2 SSE 

Simulation Lab: F: 9:00-9:50 am – Programming Studio 

Course Outline

SYLLABUS (Updated)**

 

 

Lectures

The books referred to in suggested readings are

PW: Wilmott. P, Paul Wilmott on Quantitative Finance, Wiley 2006

DH: Higham. D, An Introduction to Financial Option Valuation, Cambridge University Press 2004

BM: Malkiel. Burton, A Random Walk Down Wall Street, Norton 2020

 

Exams

·        Midterm Exam 2025*

o  Midterm 2025 Solution*

·       Final Exam 2025

Past Exams

·       Midterm Exam 2024

·       Final Exam 2024

 

 

Theory Lectures - Adnan Khan

 

Review of Differential Equations

Review of Probability

Review of Liner Algebra

 

Module I: Mathematical Background

Lecture 17: Exotics II

Lecture 1: Introduction

Module III: Numerical Methods

Lecture 2: Models in Finance  

Lecture 18: Introduction to Finite Differences

Lecture 3: Review of Probability

Lecture 19: Explicit Method for the Heat Equation

Lecture 4: Simulating Random Variables

Lecture 20: Explicit Scheme for the Black Scholes Equation

Lecture 5: Markov and Martingale Processes

Lecture 21: Implicit Schemes for Heat and Black Scholes

Lecture 6: From Random Walk to Weiner Process

Lecture 22: Monte Carlo Simulation

Lecture 7: Ito Calculus

Module IV: Portfolio Theory

Module II: Derivatives and the Black Scholes Framework

Lecture 23: Portfolio Theory I

Lecture 8: Introduction to Financial Instruments

Lecture 24: Portfolio Theory II

Lecture 9: Financial Derivatives

Lecture 25: Portfolio Theory III

Lecture 10: Options and Strategies

Module V: Fixed Income

Lecture 11: Option Premiums

Lecture 26: Introduction to Fixed Income

Lecture 12: The Binomial Model

Lecture 27: Bond Pricing Equation

Lecture 13: Binomial Model & the CRR Formula

Lecture 28: Stochastic Interest Rate Models

Lecture 14: Black Scholes Equation - Derivation

Lecture 29: Multi-Factor Models

Lecture 15: Black Scholes Formula & the Greeks

Lecture 30: Calibration

Lecture 16: Exotics I

Annotated Notes: Fixed Income

 

 

 

Simulation Lectures - Ayesha Ahmed: These are posted on LMS

 

Interesting Articles

1.      The importance of being the Central Limit Theorem

2.      Are Stock Returns Normally Distributed? | by Tony Yiu | Towards Data Science

3.      Riaz Ahmad: Know your Ito!

4.      Karl Sigman: A short Note on Ito Stochastic Calculus*(new)

5.      Deriving the Black Scholes Equation*(new)

6.      Kolmogorov, Black & Scholes and their Equations!

7.      Methods for Constructing a Yield Curve

8.      The Market Price of Interest-rate Risk

9.      Parametric and Historic VaR

10.  Three Ways to Solve for Bond Prices

11.  Ed Thorp: A Perspective on Quantitative Finance: Models for Beating the Market

12.    Eugene Fama: Stock Price Model

13.    Hans Stoll: Put Call Parity

14.  Emanuel Derman: Critique of Black Scholes

15.    Paul Wilmott: Defending the Black Scholes Model

16.    Espen Haug: Know Your Weapon (On The Greeks)

 

Homework

Ø  Diagnostic Homework

Ø  Homework 1 - Due in class Feb 17

o   Homework 1 - Solutions

Ø  Homework 2 - Due in class March 4

o   Homework 2 - Solutions

Ø  Homework 3 - Due in class March 23

o   Homework 3 - Solutions

Ø  Homework 4 - Due in class April 23

o   Homework 4 - Solutions

Ø  Homework 5 - Due May 18  

 

 

 

 

Computer Stuff

Tutorials:

MATLAB Tutorial I

MATLAB Tutorial II

MATLAB Tutorial III

MATLAB Tutorial IV

Excel Simulations: 

Are Stock Returns Normal?

QQ Plot

Binomial Distribution

 Exponential Distribution

  Normal Distribution I

  Normal Distribution II

  Weiner Process

  Mean Reverting Process

  Geometric Brownian Motion

  Monte Carlo Pricing of European Options

VaR Calculation

MATLAB Simulations:

Central Limit Theorem*

Linear Congruential Generator*

Binomial Distribution

Exponential Distribution

Normal Distribution

Weiner Process

Mean Reverting Process

Geometric Brownian Motion

Black Scholes Formula

Monte Carlo Pricing of European Options

Explicit FD Method Heat Equation

Implicit FD Method Heat Equation

Explicit FD Method Black Scholes