Gaussian Sampling

Here we sample the gaussian OU process for different mean reversion speed and number of paths.

from quantflow.sp.ou import Vasicek
from quantflow.utils import plot
import ipywidgets as widgets
import plotly.graph_objects as go

def simulate():
    pr = Vasicek(rate=0.5, kappa=kappa.value)
    paths = pr.sample(samples.value, 1, 1000)
    pdf = paths.pdf(num_bins=50)
    pdf["simulation"] = pdf["pdf"]
    pdf["analytical"] = pr.marginal(1).pdf(pdf.index)
    return pdf

def on_intensity_change(change):
    df = simulate()
    fig.data[0].x = df.index
    fig.data[0].y = df["simulation"]
    fig.data[1].x = df.index
    fig.data[1].y = df["analytical"]

kappa = widgets.FloatSlider(description="mean reversion", min=0.1, max=5)
samples = widgets.IntSlider(description="paths", min=100, max=10000, step=100)
kappa.value = 1
samples.value = 1000
kappa.observe(on_intensity_change)
samples.observe(on_intensity_change)

df = simulate()
simulation = go.Bar(x=df.index, y=df["simulation"], name="simulation")
analytical = go.Scatter(x=df.index, y=df["analytical"], name="analytical")
fig = go.FigureWidget(data=[simulation, analytical])

widgets.VBox([kappa, samples, fig])