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# NUS Math Module Review: MA4269 Mathematical Finance II

– 20% homework assignment (there were 3 assignments; most should have gotten near-full or full marks as the questions were recycled from last year’s assignments)

– 20% midterm, 1 A4 sized help sheet allowed (someone told me the median was 48/50)

– 60% final exam, 1 A4 sized help sheet allowed (they allowed 2 help sheets last year)

I obtained full marks for the homework and 49/50 for the midterm. The final exam was SO HARD (explained below).

Experience:

1. The second lecture onwards were webcasted, which is very good.

2. In order to understand this module fully, one requires a solid understanding of measure theory. However, Prof Zhou tried his best to make the content more accessible by skipping difficult proofs and explaining some concepts intuitively.

3. Honestly I feel that the topic covered in MA4269 is much more interesting than MA3269. We started by a brief revision of the last chapter of MA3269, then learned about Black Scholes PDE and Brownian motion. After that, martingale pricing (Radon-Nikodym derivative, Girsanov, representation theorem, risk-neutral measure, risk-neutral valuation, change of numeraire) was introduced. This part is where a background in measure theory proves to be useful. After the midterm, we looked at different types of options (American, barrier, Asian, lookback and multi-asset) and studied how to price them.

4. For me, the most difficult parts of this module are the American, Asian and lookback options. I found some parts (e.g. the Roger-Shi method and the mathematical arguments in the lookback option chapter) really difficult to understand that I decided not to study them for the final exam.

5. Prof Zhou teaches this module quite well. He is very knowledgeable and seems to fully know what he is teaching at all times. The webcasts are very clear. I did not go for office hours so I am not qualified to comment on this.

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