first release

first release

first release

first release

first release

Remove __pycache__ directory and update .gitignore

Remove __pycache__ directory and update .gitignore

.gitignore

@@ -1,3 +1,5 @@
 myenv/
+backtest_data/
 build/
-Extra-inf.md
+Extra-inf.md
+old/

README.md

@@ -1,10 +1,15 @@
 # **Project Overview**
 
-As a Senior Data Scientist with a PhD in Computational Physics, I have a strong foundation in analytical thinking and complex problem-solving. My current focus on finance projects stems from a deep passion for the field and a desire to apply my expertise to real-world financial challenges. Through hands-on work in finance, I am leveraging my data science skills to gain practical experience and build a robust understanding of financial systems.
+## Note:
 
-This project implements the **Black-Scholes model**, **Monte Carlo simulations** and the **Binomial Tree method** for pricing European call and put options. Real-world stock data is fetched via the **Yahoo Finance API** to compute option prices, historical volatility, and option sensitivities (the Greeks). The project also provides visualisations and comparisons of option prices using all three methods.
+🚀 I am excited to share my project focusing on This project implements the **Black-Scholes model**, **Monte Carlo simulations** and the **Binomial Tree method** for pricing European call and put options. I am developing the project further by adding backtesting, a machine learning model, and deploying the app.
 
-## **Option Pricing Model with Black-Scholes, Monte Carlo and Binomial Tree Methods**
+🎉 I believe in hands on learning. As a Senior Data Scientist with a PhD in Computational Physics, I have a strong foundation in analytical thinking and complex problem-solving. Through hands-on work in Finance, I am leveraging my data science skills to gain practical experience and build a robust understanding of financial systems.
+
+🛠️ Real-world stock data is fetched via the **Yahoo Finance API** to compute option prices, historical volatility, and option sensitivities (the Greeks). The project also provides visualisations and comparisons of option prices using all three methods.
+
+
+##  💰 **Option Pricing Model with Black-Scholes, Monte Carlo and Binomial Tree Methods**
 
 The **Black-Scholes model**, **Monte Carlo simulations**, and the **Binomial Tree method** are vital tools in financial markets for pricing options. Each method offers a distinct approach to estimating the price of European-style options, relying on parameters such as stock price, strike price, time to maturity, risk-free rate, and volatility.
 
@@ -20,7 +25,7 @@ The **Black-Scholes model**, **Monte Carlo simulations**, and the **Binomial Tre
 - Provides visualisations showing how option prices vary with stock price for **both calls and puts**.
 - **Compares** pricing results from the three methods.
 
-### **Inputs**
+###  📝 **Inputs**
 
 1. **Stock Ticker**
 2. **Stock Price (S)**
@@ -29,99 +34,111 @@ The **Black-Scholes model**, **Monte Carlo simulations**, and the **Binomial Tre
 5. **Risk-Free Rate (r)**
 6. **Market Price of the Option**
 
-### **Outputs**
-1. **Call and Put Option Prices** using the three pricing methods.
-2. **Greeks** for the call and put options.
-3. **Implied Volatility** of the option.
-4. **Plots** illustrating price changes with respect to the underlying stock price.
-5. **Comparison** of option prices from all three methods.
+###  📤 **Outputs**
 
-### **Sample Output**
+The script will generate the following output:
+- **options_report.txt**: a report file containing:
+  - **Call and Put Option Prices** using **Black-Scholes**, **Monte Carlo**, and **Binomial Tree** methods.
+  - **Greeks** and **implied volatility**.
+
+- **Plots containing:**
+  - **Comparing the predictions by different models**
+  - **Option price vs stock price (using Black Scholes model)**
+  - **Monte Carlo payoff histogram**
+  - **Monte Carlo convergence plot**
+  - **Monte Carlo paths**
+
+#### **Sample report file**
 
 ```
-Options Pricing and Greeks Calculation Report:
-----------------------------------
-
-1. User Inputs:
-- Stock Ticker: AAPL
-- Stock Price (S): 191.8
-- Strike Price (K): 207.5
-- Days to Expiration: 7 days
-- Risk-Free Rate (r): 5.00%
-- Market Price of the Option: 22.25
-
-2. Calculated Intermediate Values:
-- Time to Maturity (T): 0.0192 years
-- Historical Volatility (σ): 19.95%
-
-3. Option Prices:
-- Option Price (Black-Scholes): 15.50
-- Option Price (Monte Carlo): 15.46
-- Option Price (Binomial Tree): 15.50
-
-4. Greeks:
-- Delta: -0.9974
-- Gamma: 0.0015
-- Vega: 0.2113
-- Theta: 9.2415
-- Rho: -3.9663
-
-5. Implied Volatility Calculation:
-- Implied Volatility (IV): 118.69%
+
+  Options Pricing and Greeks Calculation Report
+
+  1. User Inputs:
+  - Option type: call
+  - Stock Ticker: AAPL
+  - Stock Price (S): 226.5
+  - Strike Price (K): 207.5
+  - Days to Expiration: 7 days
+  - Risk-Free Rate (r): 5.00%
+  - Market Price of the Option: 22.25
+  - Start and end date for calculating Historical Volatility: 2023-01-01 - 2024-09-24
+
+
+  2. Calculated Intermediate Values:
+  - Time to Maturity (T): 0.0192 years
+  - Historical Volatility (σ): 21.91%
+
+  3. Option Prices:
+  - Option Price (Black-Scholes): 19.17
+  - Option Price (Monte Carlo): 19.24
+  - Option Price (Binomial Tree): 19.17
+
+  4. Greeks:
+  - Delta: 0.9983
+  - Gamma: 0.0008
+  - Vega: 0.1710
+  - Theta: -11.3226
+  - Rho: 3.9682
+
+  5. Implied Volatility Calculation:
+  - Implied Volatility (IV): 82.16%
+  
     
 ```
+#### **Sample of Option vs Stock price plot using Black-Scholes model**
 
-## **Project Structure**
+![Option_price_vs_stock](/output/Option_price_vs_stock_price.png)
+
+#### **Sample of Monte Carlo paths and convergence plot**
+
+![Monte_Carlo_Paths](/output/Monte_Carlo_Paths.png)
+![Convergence_Plot](/output/Convergence_Plot.png)
+
+
+## 📂 **Project Structure**
 
 ```
 .
-├── main.py        # Main Python script for the project
+├── option_pricing.py        # Main Python script for the project
+├── option_pricing_app.py    # Streamlit app
 ├── setup.py        # Setup Python script to install the required libraries
 ├── README.md                        # This README file
 ├── output                       # Output folder containing the reports and plots
 ```
 
-## **Customisation**
+## ⚙️ **Customisation**
 You can customise this project by:
 - Changing the **stock ticker** (e.g., from `AAPL` to `MSFT`).
 - Modifying the **strike price**, **risk-free rate**, **time to maturity**, or **volatility**.
 - Adjusting the number of **simulations** for the Monte Carlo method or the number of **steps** for the Binomial Tree method.
 
 
-## **How to Run the Project**
+##  🎓 **How to Run the Project**
 
 1. Clone the repository.
 2. Install the following Python setup file including the necessary libraries:
 
 ```bash
 python setup.py install
 ```
-3. Execute the Python code `main.py` or the Jupyter Notebook script `main.ipynb`.
+3. Execute the Python code `option_pricing.py` or the Jupyter Notebook script `option_pricing.ipynb`.
 
 
-### **Example Output**
-The script will generate the following output:
-- **Call and Put Option Prices** using **Black-Scholes**, **Monte Carlo**, and **Binomial Tree** methods.
-- The computed **Greeks** and **implied volatility**.
-- **Option Price (call or put) vs. Stock Price** plots:
-
 ### **Parameters**
 You can modify the following parameters in the script:
 - **`ticker`**: Ticker symbol of the stock (e.g., `AAPL` for Apple).
 - **`K`**: Strike price of the option.
 - **`T`**: Time to maturity in years.
 - **`r`**: Risk-free rate (annualised).
-- **`n_simulations`**: Number of simulations for the Monte Carlo method.
-- **`n_steps`**: Number of steps in the Binomial Tree method.
-
+- **`mc_num_sim`**: Number of simulations for the Monte Carlo method.
+- **`bt_num_step`**: Number of steps in the Binomial Tree method.
 
-### **Comparison**
-The script compares prices from the **Black-Scholes**, **Monte Carlo**, and **Binomial Tree** methods, showcasing their alignment or divergence under varying market conditions and parameters like volatility and time to maturity.
 
-## **Code Explanation**
+##  📖 **Code Explanation**
 
 ### **1. Black-Scholes Model**
-The **Black-Scholes model** offers a closed-form solution for pricing European-style options, based on the assumption that stock prices follow a geometric Brownian motion.
+The **Black-Scholes model** gives a closed-form solution for pricing European-style options, based on the assumption that stock prices follow a geometric Brownian motion.
 
 #### **Formula**
 For call options:
@@ -159,30 +176,30 @@ where:
 - $Z$ is a random variable from a standard normal distribution (representing the random walk).
 
 For each simulation:
-1. Simulate the stock price over time using the GBM formula.
-2. Calculate the option **payoff** at maturity:
+1. Stock price over time is simulated using the GBM formula.
+2. Option **payoff** at maturity is calculated:
    - **Call Option**: $\max(0, S_T - K)$
    - **Put Option**: $\max(0, K - S_T)$,
 
 where $S_T$ is the simulated stock price at maturity and $K$ is the strike price.
 
-3. Discount the payoff back to present value using the risk-free rate:
+3. The payoff is discounted back to present value using the risk-free rate:
 ```math
 \text{Option Price} = \exp(-r \cdot T) \cdot \text{Average Payoff},
 ```
 
 where $T$ is the time to expiration in years.
 
-This approach is flexible and can handle a wide variety of option types, but it requires many simulations for accuracy.
+This approach is flexible and can handle a wide variety of option types though it requires many simulations for accuracy.
 
 
 ### **3. Binomial Tree Method**
 The Binomial Tree method approximates option prices by constructing a tree of possible future stock prices, calculating option prices by working backwards from the terminal nodes.
 
 #### **Steps**
-1. Divide the time to expiration into `n` intervals.
+1. Time is divided to expiration into `n` intervals.
 2. Each interval allows the stock price to increase by a factor `u` or decrease by a factor `d`.
-3. Compute option prices by working backwards using risk-neutral probabilities.
+3. Option prices are computed by working backwards using risk-neutral probabilities.
 
 ### **Greeks Explanation**
 - **$\Delta$**: Sensitivity of the option price to changes in the underlying stock price.
@@ -192,17 +209,17 @@ The Binomial Tree method approximates option prices by constructing a tree of po
 - **$\rho$**: Sensitivity of the option price to changes in the risk-free interest rate.
 
 ### **Implied Volatility Calculation**
-Implied volatility is derived from the Black-Scholes model to match the market price of an option, solved iteratively using **Brent's method**.
+Implied volatility is derived from the Black-Scholes model to match the market price of an option, calculated through trying **Newton-Raphson** first, then **Bisection**, and finally **Brent's method**. They usually converge to the same solution.
 
-### **Comparison of Methods**
-Both Monte Carlo and Binomial Tree methods provide alternative means to calculate option prices, especially for options with complex features.
+### ⚖️ **Comparison of Methods**
+All methods provide alternative means to calculate option prices, especially for options with complex features. Why not running the code and observe the comparison plot?
 
 
-## **References**
+##  📚 **References**
 - [Black-Scholes Model - Investopedia](https://www.investopedia.com/terms/b/blackscholes.asp)
 - [Monte Carlo Methods - Investopedia](https://www.investopedia.com/terms/m/montecarlosimulation.asp)
 - [Binomial Tree Model - Investopedia](https://www.investopedia.com/terms/b/binomialoptionpricing.asp)
 - [Yahoo Finance API](https://pypi.org/project/yfinance/)
 
-## **License**
+## 📜 **License**
 This project is open-source and available under the [MIT License](LICENSE).