## MAS462 Financial Mathematics

Note: This is an old module occurrence.

You may wish to visit the module list for information on current teaching.

 Semester 1, 2014/15 10 Credits Lecturer: Dr Moty Katzman Home page Reading List Aims Assessment Full Syllabus

The discovery of the Capital Asset Pricing Model by William Sharpe in the 1960's and the Black-Scholes option pricing formula a decade later mark the beginning of a very fruitful interaction between mathematics and finance. The latter obtained new powerful analytical tools while the former saw its knowledge applied in new and surprising ways. (A key result used in the derivation of the Black-Scholes formula, Ito's Lemma, was first applied to guide missiles to their targets; hence the title `rocket science' applied to financial mathematics). This course describes the mathematical ideas behind these developments together with their applications in modern finance, and includes a computational project where students further explore some of the ideas of option pricing.

Prerequisites: MAS205 (Statistics Core)
Not with: MAS362 (Financial Mathematics)
No other modules have this module as a prerequisite.

## Aims

• To introduce students to the mathematical ideas and methods used in finance.
• To familiarise students with financial instruments such as shares, bonds, forward contracts, futures and options.
• To familiarise students with the notion of arbitrage and the notion of no-arbitrage pricing.
• To introduce the binomial tree and geometric Brownian motion models for stock prices.
• To familiarise students with the Black-Scholes option pricing method.
• To introduce the Capital Asset Pricing Model.

20 lectures, no tutorials

## Assessment

One formal 2.5 hour written examination [70%]. Format: 4 questions from 4. Project [30%].

## Full syllabus

Interest rates, bonds and yield curves. (2 lectures)

Forward and Futures contracts. (3 lectures)
Options. (3 lectures)
Binomial trees and risk neutral valuation. (2 lectures)
Review of probability. (1 lecture)
The stochastic process followed by stock prices. (2 lectures)
The Black-Scholes pricing formulas. (2 lectures)
Portfolio theory. (2 lectures)
The Capital Asset Pricing Model. (3 lectures)