Research
Stochastic Option Pricing
Four option-pricing models fitted to NIFTY 50, compared head to head, with fast FFT pricing.
- When
- Jan – Apr 2026
- Crew
- Team of 3
- Domain
- Quant
- Stack
- Python · Maximum likelihood · FFT · Stochastic volatility
OP-05 · TelemetrySim
- 4
- Models
- 1,721
- Daily returns
- Bates
- Best fit
Mission report
The problem
Black–Scholes assumes markets move smoothly. They don't, and the cost shows up most in out-of-the-money puts.
What I built
As a lab project with two classmates, I implemented Black–Scholes, Merton jump-diffusion, Heston and Bates, and calibrated each by maximum likelihood on 1,721 daily NIFTY 50 returns from 2018 to 2024. Pricing uses convolution FFT following Gao & Hyndman (2025), with an error-bound analysis.
Result
Bates fit best on both AIC and BIC. Black–Scholes underpriced out-of-the-money puts by 20% to over 100%.