jason-ash / pyesg Goto Github PK

#44 removed the JointStochasticProcess class and consolidated everything into the StochasticProcess abstract base class. I added a dim parameter to this class that is currently unused. I think this parameter should be used (at least) to validate the x0 arrays that are passed to the class methods, and also to ensure the correlation matrix (if required) is the correct size.

Example:

>>> from scipy import stats
>>> import xarray as xr
>>> out = xr.DataArray(
...     data=stats.norm.rvs(size=(100, 30*12+1, 4), random_state=42),
...     coords=[range(100), range(361), ['SPX', 'RTY', 'NDX', 'EST']],
...     dims=['scenario', 'step', 'index']
... )
>>> idx = dict(scenario=0, index='SPX')
>>> out.loc[idx]
<xarray.DataArray (step: 361)>
array([ 0.496714, -0.234153, -0.469474, ...,  0.860473, -0.248691,  0.662881])
Coordinates:
    scenario  int32 0
  * step      (step) int32 0 1 2 3 4 5 6 7 8 ... 353 354 355 356 357 358 359 360
    index     <U3 'SPX'

Most stochastic models will probably fall under a base class we could call DiffusionProcess. Would provide shared functionality for any stochastic model, such as Vasicek, CIR, Hull-White, etc.

class DiffusionProcess:
    """Base class for stochastic simulation models"""

Open question: will there need to be a distinction between models that have a defined transition density vs. ones that don't?

In #30 I've noticed that the generic Union[float, np.ndarray] is becoming less accurate. While most functions should be able to accept list-like or float inputs, I think all functions should probably return numpy arrays as a default.

I found this package when asking Cursor about esg models that can generate customized skewness stock returns, it responded:

`from pyesg import ESG

params = {
'n_scenarios': 1000,
'n_years': 10,
'dt': 1/12,
'r0': 0.02,
'vol': 0.01,
'mean_reversion': 0.1,
'lambda_': 0.1,
'sigma': 0.01,
'rho': 0.5,
'skew': -0.5
}
esg = ESG('GBM', params)
`

Looks like in some version, this package can generate GBM with customized skewness, but I could not find it in the current version.

Is there any solution?

For example, in the Hull-White model.

StochasticProcess should accept x0 as lots of types: float, int, list[int], list[float], and np.ndarray. Add a method that can handle all of these and return an np.ndarray instead, so the methods can uniformly operate on known numpy arrays and return numpy arrays as outputs.

The dt argument in self.standard_deviation here is set as a fixed 1.0, rather than being the variable dt. Simple fix. Also should add some comments about what exactly is happening in this einsum.

Hey,

do you mean by 'built-in plotting' to simply call a method that can plot results obtained from a stochastic process (such as Geometric Brownian Motion)?

I have conducted extensive outlier analysis of stochastic simulations in life insurance and could imagine that for instance an automatic plotting of the mean, quantiles and some other key information (or moments) could indeed make using the library more useful.

What do you think? I am new to contributing and I would love to be able to add something useful to this package.

Kind regards,
Andreas

One question,

Looks like you are trying to apply sth like eq(7) of http://www.frouah.com/finance%20notes/Euler%20and%20Milstein%20Discretization.pdf?
If so, the formula of GBM (that you are using in the code) maybe sth like:
Geometric Brownian Motion: X_{k+1} = X_k*exp((μ - δ - (1/2)*σ**2)dt + σdW)?

And do you have any suggested documentation for the Euler scheme you are using (like what is the apply function, etc)?

Thanks!

Hi Jason - this is a newbie question. I'm trying to run the following code in Jupyter notebook but I'm not getting any output...it just sits there like I never pressed run.

import pyesg

model = pyesg.GeometricBrownianMotion(mu = 0.05, sigma = 0.2)

x0 = 100
dt = 1
n_scenarios = 1000
n_steps = 60
random_state = 123

results = model.scenarios(x0, dt, n_scenarios, n_steps, random_state)

I've tried other code to test there's nothing else wrong but I don't think there is. For example, when I run...

import pyesg

mu = 0.05
sigma = 0.2
x0 = 100
dt = 10

pyesg.GeometricBrownianMotion(mu, sigma).expectation(x0, dt)

...I get:
array([134.98588076])

Can you help?!

Wijdan

I noticed a decimal shift error in 2019 3-month US treasuries within ust_historical_csv. Updated these 12 values and added 2020 UST.
ust_historical.zip

Currently the StochasticProcess classes process a single timestep at once. They should be able to parallelize these steps across any number of scenarios, so we can run N scenarios very quickly.

To implement this, we should find a way to accept an array of start values and process each of their steps simultaneously. This is similar to the way scipy.stats distributions can handle multidimensional arrays to produce distribution metrics.

Hey,

Is it possible that the pypi version does not match the repo. The README.md example doesn't work and the installed package (0.1.1) look different.

Populate this validation method for each model, checking

• coefficient types
• coefficient shapes (if arrays)
• coefficient value ranges (e.g. positive-only, or relational constraints as in the CIR model.)
• matrix properties (e.g. for correlation matrices)

Then ensure the _validate_coefs is called at the appropriate time before other methods, e.g. sample are able to be called.

Improve test coverage by using the hypothesis library.

For example, the two-factor Vasicek model or the two-factor Hull-White model.

Allow stochastic models to be fit with historical data. This seems like a BIG task, but important.

Ideas that may be relevant:

• use MLE where appropriate, or possible
• use the "Exact Algorithm"
• add a _transition_density property to each model, where it exists

Extend the current implementation of a DiffusionProcess to be able to simulate multiple indices (e.g. S&P 500, Russell 2000, etc.).

This probably means the signature of the sampling algorithm might need to change to include an extra parameter: n_indices.

Hi Jason - this is a newbie question. I'm trying to run the following code in Jupyter notebook but I'm not getting any output...it just sits there like I never pressed run.

import pyesg

model = pyesg.GeometricBrownianMotion(mu = 0.05, sigma = 0.2)

x0 = 100
dt = 1
n_scenarios = 1000
n_steps = 60
random_state = 123

results = model.scenarios(x0, dt, n_scenarios, n_steps, random_state)

I've tried other code to test there's nothing else wrong but I don't think there is. For example, when I run...

import pyesg

mu = 0.05
sigma = 0.2
x0 = 100
dt = 10

pyesg.GeometricBrownianMotion(mu, sigma).expectation(x0, dt)

...I get:
array([134.98588076])

Can you help?! I'm quite new to Python so I'm pretty sure I'm just make an obvious mistake somewhere.

Wijdan

I think this is incorrect. out[0] here is the change in log value of x0[0], but then we apply the min and max as nominal rates. This doesn't feel right to me - should be corrected, and tests added to confirm the floors and caps work as expected.

Hey,

would it potentially make sense to include a more thorough tutorial on how to make use of the existing stochastic processes that you have already defined?

Kind regards,
Andreas

Would be nice to be able to plot scenarios for a given model.

Should probably make sense to be able to convert tuples to np.arrays as well.

the 3Month value seems 100x greater ?

Cox-Ingersoll-Ross

import numpy as np

def cir(r, k, theta, sigma, dt):
    return r + k*(theta - r) + sigma*r**0.5*dt**0.5*np.random.randn()

Hi Jason,
I am Shiva and I am working on scenario generation on solar PV generation forecast to address uncertainty between the actual and prediction.

I tried to use "pyesg" - Geometric Brownian Motion to generate scenerios.

I am using google colab environment for my research work and I installed the package using "!pip install pyesg"

I tried your example in my google colab space and it throws error. Please advice me to solve the issue.

I have attached screen shot below,