## MAS362 Financial Mathematics

Note: Information for future academic years is provisional. Timetable information and teaching staff are especially likely to change, but other details may also be altered, some courses may not run at all, and other courses may be added.

 Semester 1, 2022/23 10 Credits Lecturer: Dr Dimitrios Roxanas Timetable Reading List Aims Outcomes Teaching Methods 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.

Prerequisites: MAS223 (Statistical Inference and Modelling)
Not with: MAS462 (Financial Mathematics)
No other modules have this module as a prerequisite.

## Outline syllabus

• Introduction, arbitrage, forward and futures contracts
• Options, binomial trees, risk-neutral valuation
• Brownian motion and share prices, the Black-Scholes analysis
• Portfolio theory, the Capital Asset Pricing Model.

## 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.

## Teaching methods

In addition to lectures and office hours, we will have an (optional) tutorial every few weeks, on Thursday 16.00-17.00. Dates for the tutorials: 30/9, 21/10, 4/11, 25/11, 16/12.

Office Hours: Wednesday 11am-12pm (on Blackboard, there is a link on the left-hand-side panel) and by appointment.
You will be given 3 non-assessed homeworks (marked and returned for feedback). They will be released (on Crowdmark) on 12/10, 4/11, and 2/12 respectively. These dates are tentative.

20 lectures, no tutorials

## Assessment

One formal 2.5 hour written examination [100%]. Format: 4 questions from 4.

## 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)