- Student Records
Programme & Unit Catalogues

MA50089: Stochastic processes & finance

Follow this link for further information on academic years Academic Year: 2018/9
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period:
Semester 2
Further information on unit assessment Assessment Summary: CW 25%, EX 75%
Further information on unit assessment Assessment Detail:
  • Coursework (CW 25%)
  • Examination (EX 75%)
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA50125
Further information on descriptions Description: Aims:
To present the Black-Scholes-Merton approach to pricing financial derivatives, and the mathematical results which underpin this theory. To perform simple calculations to compute certain quantities relating to Brownian motion, and to understand how these quantities can be important in pricing financial derivatives.

Learning Outcomes:
On completing the course, students should be able to:
* Compute the prices of options in the one-period Binomial model
* Explain how the principle of arbitrage can be used in determining the prices of derivative contracts
* Define a Brownian motion, and determine basic properties of Brownian motion
* Use the martingale property to find important quantities relating to Brownian motion
* Apply the Black-Scholes formula to find the price of a European Call option
* Demonstrate critical thinking and an in-depth understanding of some aspects of stochastic processes.

Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials) A (in coursework).

Discrete time: trading portfolio, Binomial model, arbitrage, derivative pricing using arbitrage. Radon-Nikodym derivative, change of measure, Fundamental Theorem of Asset pricing.
Brownian motion: definition, basic properties, reflection principle. Using related martingales, and computing quantitative properties of Brownian motion.
Sketch introduction to Stochastic Integration and stochastic differential equations. Ito's Lemma, Girsanov's Theorem.
Black-Scholes model: Geometric Brownian motion as a model for asset prices, risk-neutral measure,
European call price formula, Fundamental Theorem of Asset pricing.
Further information on programme availabilityProgramme availability:

MA50089 is Optional on the following programmes:

Department of Mathematical Sciences