This module introduces the learner to the mathematics of pricing, construction and hedging of derivative securities. Discrete-time models form the foundation of our treatment with concepts such as change-of-measure and martingales introduced within this framework. Option pricing will be considered from the perspectives of replication and risk-neutral expectation. Parity relationships and binomial pricing methods will be explored for European and American options. Multi-step binomial models will be considered for standard and exotic options. A discrete treatment of Monte-Carlo methods to path-independent and path-dependent options will be considered.
Expected value versus arbitrage pricing
Expected value versus arbitrage pricing, time value of money
Binomial trees
Binomial model, derivative synthesis, replication, Arrow-Debreu securities, risk-neutral measure
Martingales, change-of-measure, representation
Stochastic processes, filtrations, claims, conditional expectation, martingales, binomial representation theorem
Binomial option pricing
Vanilla and exotic option pricing on multi-step binomial lattices, pricing inequalities
Discrete time Monte-Carlo pricing
Martingale measure pricing, confidence intervals for option prices
Lectures supported by problem-solving sessions and the use of mathematical software packages where applicable.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 100 |