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# NUS Math Module Review: MA5248 Stochastic Analysis in Mathematical Finance

– 10% Homework (3 homeworks, best of 2, I got 10/10 for this component)

– 30% In-class tests, open book (3 of them, best of 2, I got 25/30 for this component)

– 60% Final examination, 1 A4 sized helpsheet.

Experience:

– This module is manageable, provided that you have taken MA4269 before this. This module could be renamed Mathematical Finance 3 due to its nature. This module goes deep into the stochastic calculus parts in MA4269 that were previously skipped or discussed very briefly. The structure of the course is also similar, starting with a detailed review about probability concepts, followed by an in-depth discussion about Brownian motion. Lecture 3 onwards is where it gets more theoretical. The quadratic variation of brownian motion would be derived in a rigorous way, which is different from 4269. Stochastic integrals would then be elaborated on, along with its properties. Ito’s lemma would be used again, and in this module, if in doubt, apply Ito’s lemma. Stochastic differential equations would be introduced, followed by the Black Scholes PDE. Next, Girsanov’s theorem would be elaborated on, followed by change of numeraire. The concepts are the same as 4269 but the notation is quite different. The module ends with barrier options and pricing of exchange options, greeks.

– Prof Zhou has been teaching this module for 4 to 5 times in a row now. He is very experienced in teaching this module and even tries to inject humour into the lecture. Prof Zhou explains concepts in a clear manner and tries his best to use analogies from simpler mathematical concepts to explain the more advanced concepts in this module. The lecture notes are also quite comprehensive and I recommend reading them before attending the lecture because some parts can get a little confusing.

– There are no tutorials for postgraduate modules but Prof Zhou provides some small exercises in each set of lecture notes to practice on applying the concepts. He also assigns homework which allows us to practice the concepts learnt.

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