Stochastic Modelling for Retirement Products

This note closes the loop between the course's two halves: the retirement products of fund management and retirement investing in Australia embed option guarantees, and pricing them is Monte Carlo work straight out of Note 3 — with two twists that make it interesting. First, the premium is not paid upfront but as an ongoing fee on the account balance, so the fair fee must be found iteratively (the fee changes the account paths, which change the claims, which change the fair fee). Second, the measure question of Note 1 returns with force: guarantees are priced and hedged under $\mathbb{Q}$ but planned and tested under $\mathbb{P}$, and using the wrong measure for the task is a classic error. The note ends with hedging at institutional scale — the delta-hedging argument of Note 1,, grown up.

Learning objectives. By the end of this note you should be able to: