Math I should learn for derivatives pricing and financial engineering in general
Hello,
Would like to ask some guidance from the WSO community.
I am working as a junior sales for flow derivatives at a BB. The more I get to know about the industry, the more I feel that knowledge in financial engineering (especially derivatives pricing) is essential.
Yes I can complete all my sales tasks without knowing any of the technicalities behind the products, but that seriously limits my opportunities and mobilities.
So, I decided that I want to learn about derivatives pricing and financial engineering in general.
However, as ashamed as I am to say, my math abilities seem quite insufficient to tackle most topics that I want to learn.
A bit of background - the last time I take an actual math class, I was still in high school. I was actually in an AP math class and did college level calculus 1 and stuff (but forgot most of it). And I majored poli sci in college (why/how I got into derivatives sales in a long story).
So what math knowledge should I acquire before I delve into financial engineering stuff? Could you smart people out there give me some precise suggestions? (Please please don't just tell me "learn calculus and stats!")
My most sincere gratitude in advance.
Well get a good calculus book and get a grip on the basics then Stochastic Calculus, Integral Transforms, probability theory. All these work with a pretty solid understanding of calculus at an elementary level. If you really want to "learn" the math you have to understand calculus.
That depends entirely on how deep you intend to delve into financial engineering. For example, let's say you want to have a strong understanding of how the Black-Scholes model works. This particular model is similar to the heat equation in that it's a partial differential equation (this is an incomplete description, but bear with me). So, in order to get an understanding of partial differential equations, you'd need to take the following courses:
Calculus 1 Calculus 2 Calculus 3 Linear Algebra Ordinary Differential Equations Partial Differential Equations
With the exception of "Partial Differential Equations" these tend to be freshman and sophomore level courses for students pursuing a mathematics degree (some universities are different, this is just my experience). If you gain a solid understanding of the topics above, I'd say you would have a strong understanding of the Black-Scholes model. Now, if you want a more generalized understanding of pricing models, you must go much further. Others may have different ideas of what to persue (feel free to add/subtract from the following), but here's what I would suggest in addition to the above:
Probability Theory Measure Theory Functional Analysis Vector Calculus Real Analysis Stochastic Calculus
Those courses tend to be taken by juniors and seniors pursuing a mathematics degree while others (in particular, non-intro level Stochastic Calc) tend to be in the graduate levels of mathematics departments. If you can master all of the courses listed above, you'll have a strong fundamental base. That being said, it's highly unlikely that you'll need such a rigorous courseload to understand how they function in practice, as many of those courses (some of the latter group in particular) are theoretical in nature (i.e. what's called pure mathematics) and may not be necessary depending on your specific goal.
tl;dr - Probably a whole hell of a lot. But, that depends entirely on how well you want to understand them.
mikesswimn gave you a pretty comprehensive list and what is typically the prerequisites for being accepted into a MFE program, along with some programming courses (typically C++ I believe). If you just want to learn basics, you could probably short cut a lot of the ancillary material and pick up a few books with calc, pde/ode and some derivatives pricing concepts.
I think the others have given you a pretty thorough description of all the math required for an MFE program. I think there are short cuts you could take, but given your limited technical training your best bet is probably to begin with the basics and work your way up over a prolonged period of time.
The main point I wanted to get across, however, is that you will definitely need a real analysis class if your goal is to understand the basics of stochastic calculus. I took stoch calc without ever taking real analysis and I think it made the course an order of magnitude more difficult for me.
given your background, I think the list of suggestions previous posters have given are completely unrealistic and inefficient. as a math major i've taken the standard graduate real analysis and probability etc but that's def not necessary.
you need to get a stronger grasp of probability and a general intuition for how a mathematical model works. look up backward induction and binomial trees, maybe random walks.
that captures the idea of pricing and how to find expected value: you multiply the value of a node by the probability that you reach the node.
it's too bad that when you wiki an article you'll get bombarded with intimidating terms like "martingale, filtered probability space, girsanov theorem..." when really these are simple ideas dressed in intimidating language (which can take a lot of work to master though)
I agree with you to a point, but don't you think to best way to get a "stronger grasp of probability and a general intuition for how a mathematical model works" is to actually go through some formal training? I'm not saying he has to go through a complete undergrad/grad math curriculum, but a few classes beyond high school math are certainly necessary.
On reflection, the OP may want to go to a text that leaves a lot of the math off the table and dive right into financial engineering problems. Then as you come across mathematical road blocks you can learn those techniques on a case by case basis. I would recommend Luenberger's "Investment Science" which does a pretty thorough job of binomial derivative pricing in the second half of the book. However, it never delves too deeply in continuous time pricing and all the math that entails.
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