Re: [sympy] Chase Relock - GSOC interest in Group Theory, ODEs, or possibly Statistical Finance

[Matthew Rocklin]

Hi Chase, 

Thanks for your interest.  Many of the topics you bring up are definitely of interest to us.

In my experience students who present and run with their own topics often produce good results, so, if you have a particular interest in quantitative finance then it's good to push on that.  However, specific application-focused projects tend to see a bit less use than general mathematical infrastructure; they are only used by their domain rather than re-used by lots of domains.  I wonder, are there some interesting pieces of mathematics on which finance depends that you could implement instead?  In other words is it possible to break down finance into various general mathematical pieces, implement/improve those, and then finally cap the project with a very thin finance layer?

That being said, my understanding is that the Python/finance world is pretty big and our current community doesn't currently make efforts to support it in the same way that we do the sciences.  Having someone around who thought about how SymPy could benefit the financial world is probably good for the project.

-Matt

On Mon, Mar 3, 2014 at 4:43 PM, Chase Relock <chase....@gmail.com> wrote:

Hi all, 

My name is Chase Relock

I'm current a senior in mathematics at UC Berkeley and have experience programming python primarily. I've done two classes in pure group theory and have a lot of resources at my disposal on group theory that make it a viable choice for me. I've also done a high level ODE theory course which I've retained a lot of material from and could contribute. Ideally though I might be interested in implementing some statistical finance module. A built in black-scholes model and the calculation of implied volatility (Often something goal-seeked in excel) could be a place to start. I have also developed some interesting results from this question I initially asked on Quant StackExchange HERE that allow for a very nice symbolic construction of a portfolio from a given payoff function that is more elegant than the solution proposed in the linked PDF. It would actually go hand-in-hand with a symbolic matrix library. This is a topic I will also most likely be writing a small paper about as I find that there is an interesting argument to be made about finding a minimum collection of options that generate a portfolio. Stochastic finance also very quickly leads to the usefulness of a stochastic process module. Please let me know if anything here would actually be of interest, as I'd be very excited to implement some of these ideas.

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[F. B.]

On Tuesday, March 4, 2014 6:18:18 AM UTC+1, Chase Relock wrote:

I was looking at SymPy's matrix code and was curious if that supports symbolic computation right now or is it only numeric?

Of course you can put symbols inside sympy matrices (if that is what you mean), for numeric-only ones, have a look at numpy (technically numpy could be forced to use symbols, but it's not straightforward).
 

As for some of the individual pieces, I think the following are important concepts needed in financial statistics that I am unsure SymPy currently has functionality for:

kernel density estimators for PDFs

Empirical distribution functions

Statistical moments

Stochastic Processes

Stochastic/Ito Calculus

Time series

Matrix decomposition (spectral, singular value)

What about introducing stochastic processes, Martingales and Ito integration (all in symbolic representation, of course)? I think that could already be a good project.

By the way, I have been using the sympy.stats module, and I get a lot of NotImplementedError, and other kinds of errors. Finishing that parts would be great, too.

[Matthew Rocklin]

> By the way, I have been using the sympy.stats module, and I get a lot of NotImplementedError, and other kinds of errors. Finishing that parts would be great, too.

I'd be curious to know how you're using it and what unimplemented features are important to you.  This discussion should maybe happen off of this thread though.

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[Matthew Rocklin]

It's still a good idea to engage the list as you think about this.  A good exercise is to mock up a little example a simple use of your proposed module.  I'm not suggesting building it, I'm suggesting showing inputs and desired outputs.

On Tue, Mar 4, 2014 at 2:12 PM, Chase Relock <chase....@gmail.com> wrote:

As I e-mailed Matt just now, I think this is a great idea. I will most likely start with the symbolic construction of Markov Chains and work from there.

-Chase

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