Thanks Femto Trader for bumping this. I took a quick look at Quantlib (and Ito) and I have to say, their numerical methods are very rudimentary (in fact, one of their methods for stochastic processes, EndPointEuler, doesn't have finite moments for its error due to KPS 1994...). For anything that isn't a Jump Process you can currently use DifferentialEquations.jl which has higher Strong order methods for solving the SDEs (with efficient adaptivity coming whenever my paper gets past peer review... short summary: mathematicians don't like computer science tools to show up in their math papers even if it makes it faster...). That's the thing though, you have to know the stochastic differential equation for the process.
That said, it would pretty trivial to use dispatch so that way you define a "GeneralizedBlackScholes" equation, when then uses dispatch to construct an SDE and apply an optimized SDE method to it. Since you can already do this manually, it would just take setting up an object and a dispatch for each process. Would this kind of ease-of-use layer for quants be something anyone is interested in? The other thing is the Forward Kolmogorov PDEs associated to the SDEs. Currently I have FEM methods for Poisson and Semilinear Heat Equations which, as with the SDEs, can define any of the processes. This has a few more fast methods than Quantlib, but it doesn't have TRBDF2 (but that would be pretty trivial to implement. If you want it let me know, it should take less than hour to modify what I have for the trapezoid rule since it's just about defining the implicit function, NLsolve handles the solving). However, for most PDEs in finance you likely don't need the general boundaries that FEM provides and so FDM (finite difference methods) can probably be used. I haven't coded it up yet because I was looking for the right implementation. I am honing in on it: ImageFiltering.jl gives a good n-dimensional LaPlacian operator (and if I can convince Tim Holy it's worthwhile, parallel/multithreaded), and I will be building up Grids.jl <https://github.com/JuliaMath/Grids.jl/issues/3> memory-efficient iterators for storing the space. This should lead to blazing fast FDM implementations where the only actual array are the independent variable (the option price) itself, so it should also be pretty memory efficient. I'll be pairing this with the standard methods but also some very recent Implicit Integrating Factor Methods (IIF) which should give a pretty large speedup over anything in Quantlib for stiff equations. Would anyone be interested in a quant ease-of-use interface over this as well? (If you'd like to help speed this up, the way to do that is to help get Grids.jl implemented. The ideas are coming together, but someone needs to throw together some prototype (which shouldn't be too difficult)) Note that Jump Processes can easily be done by using callback functions (independent jumps can be computed in advance and then use an appropriate tspan, adding the jump between the intervals. Dependent jumps just need to use a callback within to add a jump in the appropriate intervals and maybe interpolate back a bit, likely better with adaptive timestepping), and I'll probably make an API to make this easier. Let me know what you guys would like to see on the differential equation / stochastic processes side and I'll make it happen. I'm doing most of this stuff for SPDEs in stochastic systems biology, but the equations are literally the same (general SDEs and semilinear Heat equations) so I'm plowing through whatever I can. On Thursday, October 1, 2015 at 7:34:32 PM UTC-7, Christopher Alexander wrote: > > I think the Ito package is a great start, and I've forked it to work on > adding to it other features of Quantlib (as best as I can!). I'm glad > someone mentioned the InterestRates package too as I hadn't seen that. I > work at major bank in risk, and my goal is to at some point sell them on > the power of Julia (we are currently a Python/C++ shop). > > - Chris > > On Friday, September 11, 2015 at 2:05:39 AM UTC-4, Ferenc Szalma wrote: >> >> Are there any quant finance packages for Julia? I see some rudimentary >> calendar and day-counting in Ito.js for example but not much for even a >> simple yield2price or price2yield or any bond objects in Julia packages on >> GitHub. What is the best approach, using C++ function/object from Quantlib, >> to finance in Julia? >> >
