Probability, Measure & Finance (U01871)

? Credit Points : 20 ? SCQF Level : 10 ? Acronym : MAT-4-PMF

Course for final year students in Honours programmes in Mathematics.

Sigma-algebras and Borel sets. Measurable functions. Lebesgue measure and integral. Probability measure. Random variables. Distributions and distribution functions. Conditional expectation. Stochastic Processes. Martingales. Binomial Trees. Risk-neutral valuation. Cox-Ross-Rubinstein model. Stopping times. Brownian motion. Stochastic integral. Stochastic differential equations. Ito's lemma. Girsanov's theorem. Black & Scholes option pricing formula. Implied volatility. The Greeks.

Entry Requirements

? Pre-requisites : MAT-3-FiM

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Full Year (Blocks 1-4)

? Contact Teaching Time : 4 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	11:10	12:00	KB
Lecture	Thursday	11:10	12:00	KB

Summary of Intended Learning Outcomes

1. Understand the notion of probability measure and space.
2. Familiarity with conditional expectation and martingales.
3. Knowledge of the binomial tree technique applied in option pricing.
4. Familiarity with stochastic calculus.
5. Knowledge of the Black-Scholes model for European options.
6. Ability to calculate the Greeks.