COMPG012A - Financial Engineering

This database contains the 2017-18 versions of syllabuses. Syllabuses from the 2016-17 session are available here.

Note: Whilst every effort is made to keep the syllabus and assessment records correct, the precise details must be checked with the lecturer(s).


Basic probability and differential equations

Taught ByRiaz Ahmad (100%)

An introduction to the applied mathematical and computational aspects of Quantitative Finance.

Learning Outcomes

Successful application of the necessary probability and differential equation based approach to the pricing of financial derivatives; using both quantitative and numerical techniques.


1. Financial Products and Markets: Time value of money and applications. Equities, indices, foreign exchange and commodities. Futures, Forwards and Options. Payoff and P&L diagrams. Put-Call parity.

2. Stochastic Calculus: Brownian motion and properties, Itô’s lemma and Itô integral. Stochastic Differential Equations – drift and diffusion; Geometric Brownian Motion and Vasicek model.

3. Black-Scholes Model: Assumptions, PDE and pricing formulae for European calls and puts. Extending to dividends, FX and commodities. The Greeks and risk management - theta, delta, gamma, vega & rho and their role in hedging. Two factor models and multi-asset options.

4. Mathematics of early exercise: Perpetual American calls and puts; optimal exercise strategy and the smooth pasting condition.

5. Computational Finance: Solving the pricing PDEs numerically using Explicit Finite Difference Scheme.

6. Stability criteria. Introduction to Monte Carlo technique for derivative pricing. Random number generation in Excel – RAND(), NORMSINV(), simulating random walks, correlations. Examining statistical properties of stock returns.

7. Stochastic interest rate models: Fixed income world – zero coupon bonds and coupon bearing bonds; yield curves, duration and convexity. Bond Pricing Equation (BPE). Popular models for the spot rate - Vasicek, CIR, Ho & Lee and Hull & White. Solutions of the BPE.

8. Introduction to Exotics: Basic features and classification of exotic options. Simple exotics – Binaries, one-touch, power options, compound and exchange options. Weak and strong path dependency - barriers, Asians and Lookbacks. Sampling - continuous and discrete. Pricing using the PDE framework.

Method of Instruction

30 hours of lectures including 3 hours of computing sessions


The course has the following assessment components:

  • Coursework 1 (30%)
  • Coursework 2 (70%)

To pass this course, students must:

  • Obtain an overall pass mark of 50% for all sections combined.


Reading list available via the UCL Library catalogue.