.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_ch9\ch9_stoch_vol.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_ch9_ch9_stoch_vol.py: ==================================================================================================== 9.08 Stochastic volatility model ==================================================================================================== We reproduce here the figure 9.9 of the book. Utilitary functions can be found next to this file. Here, we only define codpy-related functions. .. GENERATED FROM PYTHON SOURCE LINES 10-12 Necessary Imports ------------------------ .. GENERATED FROM PYTHON SOURCE LINES 12-33 .. code-block:: Python import os import sys import matplotlib.pyplot as plt import numpy as np from codpy.kernel import Sampler try: CURRENT_DIR = os.path.dirname(os.path.abspath(__file__)) except NameError: CURRENT_DIR = os.getcwd() data_path = os.path.join(CURRENT_DIR, "data") PARENT_DIR = os.path.abspath(os.path.join(CURRENT_DIR, "..")) sys.path.insert(0, PARENT_DIR) import utils.ch9.mapping as maps from utils.ch9.market_data import retrieve_market_data from utils.ch9.path_generation import generate_paths from utils.ch9.plot_utils import display_historical_vs_generated_distribution .. GENERATED FROM PYTHON SOURCE LINES 34-36 Parameter definition ------------------------ .. GENERATED FROM PYTHON SOURCE LINES 36-51 .. code-block:: Python def get_cdpres_param(): return { "rescale_kernel": {"max": 2000, "seed": None}, "rescale": True, "grid_projection": True, "reproductibility": False, "date_format": "%d/%m/%Y", "begin_date": "01/06/2020", "end_date": "01/06/2022", "today_date": "01/06/2022", "symbols": ["AAPL", "GOOGL", "AMZN"], } .. GENERATED FROM PYTHON SOURCE LINES 52-54 Get the market data ------------------------ .. GENERATED FROM PYTHON SOURCE LINES 54-56 .. code-block:: Python params = retrieve_market_data() .. GENERATED FROM PYTHON SOURCE LINES 57-65 Defining the map ------------------------ This model augments the conditioning model by adding a stochastic volatility term : $$\begin{split} \ln X^{k+1} &= \ln X^k + \varepsilon_X^k \mid \sigma^k, \\ \sigma^{k+1} &= \sigma^k + \varepsilon_\sigma^k \mid \sigma^k, \end{split}$$ where $\varepsilon^k = (\varepsilon_X^k, \varepsilon_\sigma^k)$ are the noise components for the process and volatility, respectively. These are sampled using conditional generators $G_k^X(\cdot \mid \sigma^k)$ and $G_k^\sigma(\cdot \mid \sigma^k)$. .. GENERATED FROM PYTHON SOURCE LINES 65-76 .. code-block:: Python params["map"] = maps.composition_map( ( maps.VarConditioner_map(params), maps.add_variance_map(var_q=10), maps.log_map, maps.remove_time(), ) ) params = maps.apply_map(params) .. GENERATED FROM PYTHON SOURCE LINES 77-81 We define our sampler on the mapped data using codpy's Sampler ------------------------------------------------------------------------ You can define your own latent generator function, here we use a simple uniform distribution. But if not provided, a default one will be used by the Sampler class. .. GENERATED FROM PYTHON SOURCE LINES 81-86 .. code-block:: Python mapped_data = params["transform_h"].values generator = lambda n: np.random.uniform(size=(n, mapped_data.shape[1])) sampler = Sampler(mapped_data, latent_generator=generator) params["sampler"] = sampler .. GENERATED FROM PYTHON SOURCE LINES 87-89 We plot the original distribution vs the generated one ------------------------------------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 89-93 .. code-block:: Python params = display_historical_vs_generated_distribution(params) params["graphic"](params) plt.show() .. image-sg:: /auto_ch9/images/sphx_glr_ch9_stoch_vol_001.png :alt: ch9 stoch vol :srcset: /auto_ch9/images/sphx_glr_ch9_stoch_vol_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 94-98 Reproductibility test ------------------------------------------------ We regenerate the same path by generating from the latent representation We make sure we get the original data back. .. GENERATED FROM PYTHON SOURCE LINES 98-103 .. code-block:: Python params["reproductibility"] = True params = generate_paths(params) params["graphic"](params) plt.show() .. image-sg:: /auto_ch9/images/sphx_glr_ch9_stoch_vol_002.png :alt: ch9 stoch vol :srcset: /auto_ch9/images/sphx_glr_ch9_stoch_vol_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 104-106 We now generate a new set of 10 paths ------------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 106-112 .. code-block:: Python params["reproductibility"] = False params["Nz"] = 10 params = generate_paths(params) params["graphic"](params) plt.show() pass .. image-sg:: /auto_ch9/images/sphx_glr_ch9_stoch_vol_003.png :alt: ch9 stoch vol :srcset: /auto_ch9/images/sphx_glr_ch9_stoch_vol_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 4.266 seconds) .. _sphx_glr_download_auto_ch9_ch9_stoch_vol.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: ch9_stoch_vol.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: ch9_stoch_vol.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: ch9_stoch_vol.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_