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COMPG012 - Financial Engineering

This database contains 2016-17 versions of the syllabuses. For current versions please see here.

CodeCOMPG012
YearMSc
Prerequisites

Basic probability and differential equations

Term1
Taught ByRiaz Ahmad (100%)
Aims

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.

Content

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

Assessment

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.

Resources

Recommended Book

• Paul Wilmott, Paul Wilmott Introduces Quantitative Finance, John Wiley & Sons, 2007

Notes

• CFA Level 1 Quants (slide pack), Fitch Learning