Options Pricing Calculator Project

What this project is

A from-scratch implementation of the Black-Scholes options pricing model — the Nobel Prize-winning formula (1997) used by every options trading desk in the world. Rather than just calling a library, you build the math yourself, which is exactly what quant interviews test.

Unlike the Momentum Backtester (which simulates a strategy over time), this project is about mathematical modeling at a single point in time: given five inputs, what is a fair price for an option?

An option is a contract that gives the holder the right (but not the obligation) to buy or sell a stock at a specific price (the strike) before a certain date (expiry). The buyer pays a premium for this right. The central question: what should that premium be?

Project structure

options_calculator/
├── models/
│   ├── black_scholes.py    # Core BS formula: call/put price + all Greeks
│   └── binomial.py         # Alternative Cox-Ross-Rubinstein tree model
├── analysis/
│   ├── implied_vol.py      # Reverse Black-Scholes: find sigma from market price
│   └── visualizer.py       # Payoff diagrams, Greek surface plots, vol smile
├── main.py                 # Entry point — configure and run here
└── requirements.txt        # numpy, scipy, matplotlib

The five Black-Scholes inputs

Symbol	Name	What it means	Example
S	Stock price	What the stock costs right now	$100
K	Strike price	The price you'd buy/sell at	$105
T	Time to expiry	How long until the option expires (in years)	0.5 = 6 months
r	Risk-free rate	Return on a "safe" investment like Treasury bonds	0.04 = 4%
σ	Volatility	How wildly the stock moves (annualised)	0.20 = 20%

These five numbers go in. One fair price comes out.

Calls vs puts

Call option — right to BUY the stock at the strike price. Valuable when the stock rises above the strike.
Put option — right to SELL the stock at the strike price. Valuable when the stock falls below the strike.

Both are priced by the same Black-Scholes formula with a small variation.

The Greeks

Beyond just the price, the project computes all five Greeks — measures of how sensitive the option price is to each input changing:

Greek	Symbol	What it measures	Plain English
Delta	Δ	Sensitivity to stock price	Option gains $0.50 per $1 stock move (if Δ = 0.5)
Gamma	Γ	Rate of change of Delta	How fast your exposure shifts as stock moves
Theta	Θ	Sensitivity to time	How much value you lose each day just from time passing
Vega	V	Sensitivity to volatility	How much price changes per 1% move in volatility
Rho	ρ	Sensitivity to interest rate	How much price changes per 1% move in rates