quantgirluk / aleatory Goto Github PK

Add simulation for fBM.
Note that there are several implementations.

Very nice package! I'm learning stochastic calculus and this is a really cool tool!

I found a small bug:
The paths plotted by SPExplicit.draw() are colored to match the histogram bin that their final point falls into.
If we plot N=3 or fewer paths, then we set n_bins = int(np.sqrt(N)) <= 1, and then this logic which helps set the path colors:

bin_centers = 0.5 * (bins[:-1] + bins[1:])
col = bin_centers - min(bin_centers)  # scale values to interval [0,1]
col /= max(col)

results in a divide by zero

/Users/alexrubin/code/aleatory/aleatory/utils/utils.py:76: RuntimeWarning: invalid value encountered in divide
    col /= max(col)

because col == [0.].

It seems like the 3 lines of logic above could be replaced by col = np.linspace(0, 1, n_bins, endpoint=True).

Modelling hashtag#short_term_interest_rates sometimes requires the hashtag#stochastic_model to be defined as the solution to a stochastic differential equation, so it is necessary to perform a time discretisation and then simulate the random component. Attached is an algorithm for simulating the path of a process called CKLS, which is a generalisation of several well-known processes, such as Brownian motion, the Ornstein-Uhlenbeck process, CIR, and so on.

[1] CHAN, K. C., KAROLYI, G. A., LONGSTAFF, F. A., & SANDERS, A. B. (1992).
An Empirical Comparison of Alternative Models of the Short-Term Interest Rate. The Journal of Finance, 47(3), 1209–1227.

Hi there -

Very impressive package and thank you for making public!

I had an enhancement question.

Was curious if this package is planned to support multivariate processes? If I say have X commodities following various processes, with correlated random shocks.

Say two commodities, define one as GBM and the other as UO, with 70% correlation in their random draw direction. Is something like this currently feasible or something in the future plans?

My background in stochastic processes is in R, and can only point to MASS::mvrnorm as an example of the correlated draws.

Cheers!

Hi, I liked your package, thank you!

I believe there is a mistake in the Vasicek function

def g(x, _): return self.sigma

It should be

def g(x, _): return self.sigma * x

right?