
Academic Year:  2012/3 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 
Level:  Honours (FHEQ level 6) 
Period: 
Semester 2 
Assessment:  EX 100% 
Supplementary Assessment:  MA30089 Mandatory Extra Work (where allowed by programme regulations) 
Requisites:  Before taking this unit you must take MA40125 
Description:  Aims: To present the BlackScholesMerton 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 oneperiod 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 BlackScholes formula to find the price of a European Call option. Skills: Numeracy T/F A Problem Solving T/F A Written and Spoken Communication F (in tutorials). Content: Discrete time: trading portfolio, Binomial model, arbitrage, derivative pricing using arbitrage. RadonNikodym 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. BlackScholes model: Geometric Brownian motion as a model for asset prices, riskneutral measure, European call price formula, Fundamental Theorem of Asset pricing. 
Programme availability: 
MA30089 is Optional on the following programmes:Department of Mathematical Sciences
