EXAMINATION GUIDE 2021
MATH3075 Financial Mathematics (Mainstream)
• You should know the most basic results and be familiar with relevant computational meth-
ods. You should be ready to answer computational questions regarding general single-period
market models and the CRR binomial model, and know how to use the Black-Scholes pricing
formulae for call and put options to value combinations of options.
• No aids other than standard non-programmable calculators are permitted. You should under-
stand formulae, concepts and computational techniques needed to answer typical questions,
as outlined below. The best preparation is to go through lecture notes and tutorial questions
for MATH3075.
1. Single-period model (Exercises 1 and 2 from tutorial 6)
(a) verify the arbitrage-free property and completeness of a model,
(b) describe the class of all attainable contingent claims,
(c) find the set of all risk-neutral probability measures,
(d) compute the replicating strategy and arbitrage price for a given contingent claim.
2. The CRR model: European claims (Exercise 2 from tutorial 8 and Exercise 1 from tutorial 9)
(a) compute the risk-neutral probability measure,
(b) find the replicating strategy for a given contingent claim,
(c) compute the price process for a given European claim.
3. The CRR model: American claims (Exercises 1 and 2 from tutorial 10)
(a) find the risk-neutral probability measure,
(b) compute the arbitrage price for a given American claim,
(c) find the rational exercise time for the holder of an American claim,
(d) compute the replicating strategy for the issuer of an American claim.
4. The Black-Scholes model: European claims (Exercises 1 and 2 from tutorial 11)
(a) apply the Black-Scholes formula to price European call and put options,
(b) compute the price in the Black-Scholes model of a given path-independent European
claim with a piecewise linear payoff through a decomposition into a combination of put
and call options,
(c) analyse the asymptotic properties of the Black-Scholes price of call and put options and
hence also the asymptotic properties of the price of a given path-independent European
claim.