MTH5210: Stochastic Calculus and Mathematical FInance

3x Assignments (30% - not sure) – I thought it were quite typical questions, and not too hard as well.
10x Weekly homework (10% - not sure) – Same as the above, but considering it was weekly, it was quite easy.
1x Final exam (60%) – As far as maths exams go, I thought the exam was very hard, and really stretches your knowledge. Knowing the textbook is quite essential.

This unit is very much like MTH3251 – Financial Mathematics, but with more of a focus on stochastic calculus and underlying theorems. I guess it can be seen as a self-contained course in stochastic calculus alongside a bit of financial maths if you have some basics in calculus and probability. In particular, we look at:

1)Properties of Brownian motion (the most basic continuous time stochastic process – which are random variables that move through time)
2)Ito calculus – calculus incorporating Brownian motion (Ito’s formula underlies most, if not all studies in stochastic calculus – which is taught here)
3)Stochastic differential equations – diffusion processes (applications of Ito processes in ODEs to make SDEs and PDEs – in particular, we look at conditions for which strong solutions exist for a particular SDE, and how to find them – solutions are stochastic processes that have an explicit form that incorporate Brownian motion as well, we also talk a bit about martingales in more detail, which is relevant for a lot of theoretical work)
4)Weak solutions to SDEs – there are two ways of estimating weak solutions when strong solutions are not available, change of time, and change of probability measure, for which we investigate them here. The crux of it is just to define a new Brownian motion that makes the SDE solvable explicitly.
5)Applications to finance – we go through this very briefly, mainly discussion on applying the above concepts on asset pricing theorems and option pricing. These are all quite basic, but interested students can extend these concepts from these basics to complex methods – such as more complex derivative pricing, and modelling. (Applications are taught in MTH5520 – interest rate modelling where we look at stochastic calculus applied in bond markets).

I would recommend this unit compared to MTH3251, although the undergrad unit helps a lot with making this unit bearable. This unit goes much deeper into stochastic processes in continuous time and can be very interesting once you know where and why the mathematics is used in real-life applications – something the maths department doesn’t do very well tbh. The unit that is a straightforward extension to this is MTH5520 – Interest Rate Modelling, which uses stochastic calculus as well, and I find that doing MTH5210 makes the content there more bearable too, compared to a lot of students who only did MTH3251. The concepts stick easier, and it’s much more interesting that way.

Professor Fima Klebaner – he’s a very good and clear lecturer, clearly very experienced in teaching this unit (he’s also the author of the prescribed textbook), sets easy assignments too (the exam was a different story but it scales well)

Several

4 out of 5

Yes, with screen capture

Introduction to Stochastic Calculus with Applications – Klebaner – definitely a very important text because the lecturer is the author of this textbook, and he uses the content within the textbook very heavily instead of using slides or course notes (more typical for undergraduate Students)

2x 1 hour lectures
1x 1 hour tutorial

S1 2021

98 HD