Project Overview

Accessible here: defivolatilitysurface.streamlit.app

This repository contains an interactive Streamlit web application that calculates and visualizes implied volatility surfaces for cryptocurrency options. The application uses real-time on-chain data from Deribit for over 700 options and applies a Black-Scholes-based model to compute implied volatility with the Newton-Raphson method, leveraging Vega for iterative convergence. Users can adjust three parameters and view the implied volatility surface through a 3D Plotly plot, then connects to the GBT-4o-Mini model via API to analyze and generate optimal trading strategies based on the cacluted Implied volatility.

Features

• Real-time Data: Retrieves data for 700+ cryptocurrency options using the Deribit API.
• Advanced Volatility Calculations: Implements a Black-Scholes model with Newton-Raphson and Vega for iterative convergence on highly volatile assets.
• Interactive 3D Visualization: Provides a customizable 3D surface plot for implied volatility across multiple parameters.
• Trading Strategies for BTC Option: Trading strategies generated from real-time data using OpenAI's GPT-4 Mini Model.

Repository Structure

Notebooks

• 1. Data-Preprocessing.ipynb: Contains the data cleaning and preprocessing steps required for preparing the on-chain options data.
• 2. (BTC) - Exploratory Data Analysis.ipynb: Conducts exploratory data analysis for Bitcoin options, focusing on the Vega-based approach for implied volatility.
• 3. implied_volatility_surface.ipynb: This notebook calculates the implied volatility surface using a Black-Scholes-based model and visualizes it with Plotly.
• 4. vs.py: Queries data, calculates implied volatility, and visualizes the volatility surface, hosting the results interactively on Streamlit.

Formulas Used

1. Black-Scholes Model for Option Pricing

The Black-Scholes formula is used to price European-style options and forms the basis for implied volatility calculation. For a call option, the Black-Scholes price $C$ is given by:

$$ C = S_0 \cdot N(d_1) - X \cdot e^{-rT} \cdot N(d_2) $$

where:

• $S_0$ = current price of the underlying asset
• $X$ = strike price of the option
• $T$ = time to maturity of the option (in years)
• $r$ = risk-free interest rate
• $N(\cdot)$ = cumulative distribution function of the standard normal distribution

The terms $d_1$ and $d_2$ are calculated as:

$$ d_1 = \frac{\ln\left(\frac{S_0}{X}\right) + \left(r + \frac{\sigma^2}{2}\right)T}{\sigma \sqrt{T}} $$

$$ d_2 = d_1 - \sigma \sqrt{T} $$

For put options, the formula changes slightly to:

$$ P = X \cdot e^{-rT} \cdot N(-d_2) - S_0 \cdot N(-d_1) $$

2. Implied Volatility and the Newton-Raphson Method

Implied volatility ($\sigma_{\text{impl}}$) is the value of $\sigma$ that matches the observed option price $C_{\text{obs}}$. The Newton-Raphson method approximates it iteratively:

$$ \sigma_{\text{new}} = \sigma_{\text{old}} - \frac{f(\sigma_{\text{old}})}{f'(\sigma_{\text{old}})} $$

where:

• $f(\sigma) = C(\sigma) - C_{\text{obs}}$
• $f'(\sigma)$ = Vega (partial derivative of the option price with respect to volatility)

3. Vega Calculation

Vega, used in iterative convergence, is given by:

$$ \text{Vega} = S_0 \cdot \sqrt{T} \cdot N'(d_1) $$

where $N'(d_1)$ is the probability density function of the standard normal distribution evaluated at $d_1$.

4. Implied Volatility Adjustment Using Newton-Raphson

Using Vega, we adjust volatility $\sigma$ iteratively until the calculated option price $C(\sigma)$ closely matches $C_{\text{obs}}$:

$$ \sigma_{\text{new}} = \sigma_{\text{old}} - \frac{C(\sigma_{\text{old}}) - C_{\text{obs}}}{\text{Vega}} $$

Usage

• Calculation & Visualization: After running the app, use the interactive interface to input parameters and generate the implied volatility surface.