COMPG012 - Financial Engineering
This database contains 2016-17 versions of the syllabuses. For current versions please see here.
Basic probability and differential equations
|Taught By||Riaz Ahmad (100%)|
An introduction to the applied mathematical and computational aspects of Quantitative Finance.
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. Binomial model: Key assumptions. Delta hedging and no arbitrage. Risk-neutral probability and replicating portfolio. Single step and multi-period model. European and American options.
4. 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.
5. Mathematics of early exercise: Perpetual American calls and puts; optimal exercise strategy and the smooth pasting condition.
6. Computational Finance: Solving the pricing PDEs numerically using Explicit Finite Difference Scheme.
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:
• Assessed assignments (30%)
• 2.5 hour written examination in the summer (70%)
To pass this course, students must:
• Obtain an overall pass mark of 50% for all sections combined.
• Paul Wilmott, Paul Wilmott Introduces Quantitative Finance, John Wiley & Sons, 2007
• CFA Level 1 Quants (slide pack), Fitch Learning