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Time Series Derivatives Analysis Report

Last Update September 16, 2021

Matteo Bottacini, [email protected]

Project description

In this report are show the results obtained for the Time-Series Derivatives Analysis.

The codes described are in ../deliverables/run-time-series-analysis.py which is the only script you need to run to perform the analysis. The images and the tables are in ../reports/.

Note: all the images in this GitHub repo are .png instead of .pdf. The reason is to make it easier for GitHub to render the results.

Table of contents

  1. Main Variables
  2. Create the Environment: directories and sub-directories
  3. Load data and data pre-processing
  4. Underlying analytics
  5. Implied volatility historical distribution
  6. Model calibratio

Main variables

The first step is to declare the main variables. Feel free to change this setting.

# main variables
local_folder = 'deliverables'  # folder where this script is run
min_time_interval = 5          # first model to be calibrated
max_time_interval = 1440       # last model to be calibrated 
step = 5                       # step between a model and the following one
atm_skew = 1                   # Skew of an ATM option
itm_skew = 1.75                # Skew of an ITM option, this will be used for modelling the volatility skew 
otm_skew = 0.25                # Skew of an OTM option, this will be used for modelling the volatility skew

Create the Environment: directories and sub-directories

The second step is to create the environment to store the results using the self-function create_env().

# import modules
from TimeSeriesAnalysis.src.utils import *

# create environment
create_env(local_folder=local_folder,
           min_time_interval=min_time_interval, max_time_interval=max_time_interval, step=step)

Load data and data pre-processing

The third step is to load the data into the working environment and to pre-process them using the function load_data() for both BTC and ETH.

# import modules
from TimeSeriesAnalysis.src.utils import *

# load data
btc_data = load_data(coin='btc', cwd='TimeSeriesAnalysis/desliverables')
eth_data = load_data(coin='eth', cwd='TimeSeriesAnalysis/deliverables')

Underlying analytics

The fourth step is to analyze the underlying time-series and dynamics for both BTC and ETH using the function underlying_analytics().

# import modules
from TimeSeriesAnalysis.src.utils import *

# index price analytics
index = underlying_analytics(local_folder=local_folder, btc_data=btc_data, eth_data=eth_data)

Thus, these are the price dynamics for BTCUSD and ETHUSD:

Then, the histogram of the 5-minutes log-returns and Daily log-returns, while the descriptive summary statistics of the returns are in this table: summary.csv

Finally, the cumulative returns, 30 rolling correlation and realized volatility:

Implied Volatility historical distribution

The fifth step is to analyze the historical distribution of the market implied volatiltiy, and it is done by the function iv_distribution() for both BTC and ETH.

# import modules
from TimeSeriesAnalysis.src.utils import *

# iVol distribution analytics
iv_distribution(coin_df=btc_data, coin='BTC', local_folder=local_folder)
iv_distribution(coin_df=eth_data, coin='ETH', local_folder=local_folder)

The histograms of the observations are below, while the descriptive summary statistics of the distribution are: BTC_iv_summary.csv and ETH_iv_summary.csv.

Model calibration

The last step is to calibrate the model to estimate the implied volatility for both BTC and ETH. The function used is model_calibration():

# import modules
from TimeSeriesAnalysis.src.utils import *

# model calibration
model_calibration(coin_df=btc_data, min_time_interval=min_time_interval, max_time_interval=max_time_interval,
                  step=step, atm_skew=atm_skew, itm_skew=itm_skew, otm_skew=otm_skew,
                  local_folder='deliverables', coin='BTC')
model_calibration(coin_df=eth_data, min_time_interval=min_time_interval, max_time_interval=max_time_interval,
                  step=step, atm_skew=atm_skew, itm_skew=itm_skew, otm_skew=otm_skew,
                  local_folder='deliverables', coin='ETH')

For the purpose of this GitHub only the results from the model calibrated each 720 minutes are shown. The BTC results for this model are in BTC/720_min_calibration. The ETH results for this model are in ETH/720_min_calibration.

The model parameters' dynamics data are for BTC: BTC/720_min_calibration/data/BTC_parameters.parquet and for ETH: ETH/720_min_calibration/data/ETH_parameters.parquet. The summary of the descriptive statistics are for BTC: BTC/720_min_calibration/tables/BTC_parameters.parquet, and for ETH: ETH/720_min_calibration/tables/ETH_parameters.parquet. Then, the plots are:

The ATM implied volatility data for BTC are: BTC/720_min_calibration/data/BTC_atm_iv.parquet and for ETH: ETH/720_min_calibration/data/ETH_atm_iv.parquet. The summary of the descriptive statistics are for BTC: BTC/720_min_calibration/tables/BTC_atm_iv.parquet and for ETH: ETH/720_min_calibration/tables/ETH_atm_iv.parquet. Then, the plots are:

The implied Volatility Term-structure:

And the Volatility Skew data for BTC are: BTC/720_min_calibration/data/BTC_skew.parquet and for ETH: ETH/720_min_calibration/data/ETH_skew.parquet. The summary of the descriptive statistics are for BTC:BTC/720_min_calibration/tables/BTC_skew.parquet and for ETH: ETH/720_min_calibration/tables/ETH_skew.parquet. Then, the plots are:

This procedure has been applied to all the different calibrations.