Registration Deadline: September 20, 2026

Instructor: Dr. Riaz Ahmad, University College London

Course Dates: 
Mid-Semester Break: 
Lecture Time: 
Office Hours: 

Registration Fee:

• Students from our Principal Sponsoring & Affiliate Universities: Free
• Other Students: CAD$500

Capacity Limit: 

Format: 

Course Description

The aim of this self-contained and intensive module is to develop the partial differential equation approach to derivative pricing. This is a mathematical finance module; however, no prior knowledge of the financial markets is required.

Recommended Texts

• John Hull; Options, Futures, and Other Derivatives 9th Edition, Pearson, (2017)
• Paul Wilmott; Paul Wilmott on Quantitative Finance 2nd Edition, Wiley (2006)

Assessment

• Two programming tasks (30%)
• Closed Book Exam (70%)

Pre-requisites: Partial Differential Equations and Python programming

Detailed Syllabus

• Week 1: Preliminaries
• Review of heat equation and similarity reduction leading to the fundamental solution
• Relevant results from Ito calculus
• Week 2: Financial products and markets
• Financial instruments, markets and players
• Asset classes
• Time value of money
• Options, payoffs and derivatives terminology
• Week 3: Black-Scholes Model
• Assumptions and derivation of PDE
• Solution of PDE
• Vanilla and binary options
• Week 4: Further Black-Scholes modelling
• The greeks and their role in hedging
• Actual, historical/realised and implied volatility
• Multi-factor models
• Week 5: Exotics and structured products
• Detailed discussion of classification features of exotics
• Asians, lookbacks and barriers
• A framework for continuous sampling and pricing equation
• Updating rule
• Week 6 and 7: Numerical methods for finance
• Explicit, fully implicit and Crank-Nicolson schemes
• Upwind differencing for path dependence
• Monte Carlo methods for pricing
• Week 8 and 9: Fixed-Income modelling
• Fixed-income products and markets
• The spot rate for popular models – Vasicek and CIR
• Bond pricing equation (BPE) and market price of interest rate risk
• Tractable models and affine solution of the BPE
• Multi-factor bond pricing models
• Forward rates and HJM
• Week 10: Incomplete markets
• The pricing differential equation for stochastic volatility
• Market price of volatility risk
• Popular stoch. vol. models
• Heston model and its option pricing solution
• Jump diffusion