About The Project

This repository contains the code I used to implement my Master Thesis in which I compare the Black and Scholes pricing formula against an Artificial Neural Networks model for option pricing and delta hedging strategy.

Data

The datasets used in this project are:

• Option_characteristics.csv. Which contains the options' flag, the expiration date and the strike price.

• Index_series.csv. Which contains the time series data of the S&P 500 index, so the date the closing price and the return.

• Option_series.csv. Which contains the time series data for each individual option with bid/ask prices, volume, greeks, implied vol etc.

• Treasury_bill.csv. Which contains the time series data for the 90-day US treasury bill.

Usage

All the necessary steps in order to run this project are described in this section.

1_Preparing_data_frames.md in this R file the databases containing the option's information are merged together in one big file, the columns containing data not useful for the project are dropped and the remaining columns are renamed. After running this file, 3 new databases will be created:

• option_file. Which contains all the useful information about the option time series.
• index_series. Which differ form the original file only in the name of the variables
• treasury_bill. Which contains the time series data for the 90-day US treasury bill in percentage.

2_Compute_B&S_and_GARCH.py this python script is needed to:

• Estimate the GARCH volatility on the returns
• Compute the Black and Scholes pricing formula using different volatility windows and the GARCH volatility. After the computation the dataset rawdata.csv is created. This contain all the information about the options, the black and scholes predicted prices, GARCH volatility estimation and the different historical volatilities.

3_Split_Put_and_Call_data in this R markdown the dataset created in the previous step (rawdata.csv) is loaded. Afterwards the no further needed variables are removed and the cleaning process start:

• The dataset is divided in Call and Put. The process of removing the non representative observations differ slightely between Put and Call. After the cleaning process, 3 new datasets are exported:
  • pdata.csv which contains observations of both Put and Call options. These data will be used afterwards for visualization purposes.
  • call.csv which contains only information regarding the Call options. This is the final file used to implement all the analysis.
  • put.csv which contains only information regarding the Put options. This file is not used in this project, however the same analysis can be run also with this file in order to study the Put option instead of the Call.

4_Compute_Call_summary_table running this script compute the table which describes the moneyness distributed regarding the maturity time of the Call option.

5_Compute_data_summary this scripts plots all the descriptive graphs of the data.

6_Compute_volatility_summary this script is used to plot all the GARCH volatility performances.

7_Train_ANN with this script the Neural Network is implemented and trained

8_Evaluate_ANN running this file the comparison ANN and BSM regarding pricing prediction is obtained and the descriptive graphs are plotted

9_Comput_pricing_results_table this file groups in a table the pricing results obtained in the previous step. Furthermore, they are grouped in different groups based on moneyness, maturity and volatility

10_Compute_Hedging in this script the hedging strategy is implemented

11_Hedging_results in this script the comparison between the hedging strategy performed with the ANN model and the BSM model is printed in a table