Add plot to paths

notebooks/cir.md

@@ -37,7 +37,7 @@ The model has a close-form solution for the mean and the variance
 
 ```{code-cell} ipython3
 from quantflow.sp.cir import CIR
-pr = CIR(kappa=0.7, sigma=0.8, theta=1.2)
+pr = CIR(sigma=0.8)
 pr
 ```
 
@@ -46,23 +46,18 @@ pr.is_positive
 ```
 
 ```{code-cell} ipython3
-import plotly.express as px
-import plotly.graph_objects as go
-import pandas as pd
 p = pr.paths(10, t=1, steps=1000)
-fig = px.line(p.data)
-fig.show()
+p.plot()
 ```
 
+Sampling with a mean reversion speed five times larger
+
 ```{code-cell} ipython3
-pr.kappa = 20
-pr.sigma = 2
-pr
+pr.kappa = 5; pr
 ```
 
 ```{code-cell} ipython3
-p = pr.paths(10, t=1, steps=1000)
-px.line(p.data).show()
+pr.paths(10, t=1, steps=1000).plot()
 ```
 
 ```{code-cell} ipython3
@@ -78,7 +73,8 @@ chracteristic_fig(m, N, M).show()
 The code below show the computed PDF via FRFT and the [analytical formula](https://en.wikipedia.org/wiki/Cox%E2%80%93Ingersoll%E2%80%93Ross_model).
 
 ```{code-cell} ipython3
-dx = 8/N
+import plotly.graph_objects as go
+dx = 4/N
 r = m.pdf_from_characteristic(N, M, dx)
 fig = go.Figure()
 fig.add_trace(go.Scatter(x=r["x"], y=r["y"], mode="markers", name="computed"))

notebooks/dsp.md

@@ -16,7 +16,16 @@ kernelspec:
 
 ## Poisson Process
 
-+++
+```{code-cell} ipython3
+from quantflow.sp.poisson import PoissonProcess
+
+pr = PoissonProcess(rate=2)
+pr
+```
+
+```{code-cell} ipython3
+
+```
 
 ## Compound Poisson Process
 

notebooks/heston.md

@@ -5,15 +5,13 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.13.8
+    jupytext_version: 1.14.7
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
   name: python3
 ---
 
-+++ {"tags": []}
-
 # Heston Model and Option Pricing
 
 A very important example of time-changed Lévy process useful for option pricing is the Heston model. In this model the Lévy process is a standard Brownian motion, while the activity rate follows a CIR process. The leverage effect can be accomodated by correlating the two Brownian motions as the following equations illustrates:

quantflow/utils/paths.py

@@ -1,10 +1,15 @@
-from typing import Self
+from typing import Any, Self
 
 import numpy as np
 import pandas as pd
 from pydantic import BaseModel, ConfigDict, Field
 from scipy.integrate import cumtrapz
 
+try:
+    import plotly.express as px  # type: ignore
+except ImportError:
+    px = None
+
 
 class Paths(BaseModel):
     """Paths of a stochastic process"""
@@ -48,3 +53,8 @@ def integrate(self) -> Self:
         return self.__class__(
             t=self.t, data=cumtrapz(self.data, dx=self.dt, axis=0, initial=0)
         )
+
+    def plot(self) -> Any:
+        if px is None:
+            raise ImportError("plotly is not installed")
+        return px.line(self.data, title="Paths")