Option Pricing
Quant casefile for a derivatives toolkit that moves from Black-Scholes fundamentals to richer model assumptions and practical scenario checks.
From Black-Scholes to Heston and Merton jump diffusion.
Interactive checks for spot, strike, time, rates, and volatility without opening a notebook.
Built to teach, compare assumptions, and support fast review decisions.
Summary
Model builder, explainer, and interface designer for a compact derivatives reference.
Python, Streamlit, numerical methods, model comparison, and scenario experimentation.
Why I built it
- Black-Scholes is widely taught, but in practice it is only the entry point for how traders and analysts think about options.
- I wanted one place to compare baseline assumptions, practical limitations, and richer alternatives without hiding inside theory-only notes.
- The result became both a learning surface and a quick scenario-check tool.
Model comparison
| Model | Best used for | Main tradeoff |
|---|---|---|
| Black-Scholes | Fast baseline valuation | Assumes constant volatility and log-normal returns |
| Binomial tree | Early exercise intuition and discrete steps | Slower and more parameter sensitive |
| Monte Carlo | Flexible scenario generation | Computationally heavier |
| Heston | Stochastic volatility context | More calibration overhead |
| Merton jump diffusion | Gap-risk and jump intuition | Added model complexity |
Core inputs
- Spot price
- Strike price
- Time to expiration
- Risk-free rate
- Volatility
Greeks in practice
Sensitivity to underlying-price changes and the simplest read on directional exposure.
How quickly delta changes as the underlying moves, which matters for convexity and hedge stability.
Time decay and the cost of waiting while an option position remains open.
Sensitivity to volatility changes and how repricing can move the option even without a directional move.
Rate sensitivity, most relevant when contracts are longer-dated or rates are moving materially.
Where it helps in practice
Frame relative-value checks and compare what different assumptions imply for the same option.
Use Greeks and scenario comparisons to understand how directional and volatility risk interact.
Turn a pricing question into explicit drivers instead of treating the output as a black box.
Build intuition for when simple closed forms are enough and when richer simulation or tree methods matter.
Product links
Streamlit demo
Interactive valuation surface for comparing inputs, model behavior, and pricing outcomes.
GitHub repo
Implementation for model comparison, numerical methods, and sensitivity experimentation.
Limits and extensions
- Constant-volatility assumptions break under real surfaces.
- Jump risk, skew, and market frictions matter during event-driven periods.
- The natural extension path is implied-volatility work, richer stochastic-volatility treatment, and more visual sensitivity analysis.
References used in the study path
- Black and Scholes, 1973
- Merton, 1973
- Cox, Ross, and Rubinstein, 1979
- Hull, 2017
- Gatheral, 2006
- Cont and Tankov, 2009