04 / Systems / 2024–2025
Heston pricing and calibration.
Individual dissertation / Heston model
01 / SCOPE
Problem and
scope.
My individual dissertation investigated calibration of the Heston stochastic-volatility model to SPX option prices. Calibration repeatedly prices contracts while estimating model parameters. I compared CPU COS pricing, batched CuPy GPU pricing and a neural approximation, measuring calibration time and pricing error.
I implemented the Heston pricing and calibration pipeline: NumPy Fourier–COS pricing, batched CuPy evaluation, bounded L-BFGS-B optimisation and a ten-feature PyTorch surrogate trained on 600,000 synthetic samples.
02 / IMPLEMENTATION
Implementation
details.
- 01Filter SPX contracts
- 02COS pricing
- 03Bounded optimisation
- 04Neural surrogate
- 05Compare trade-offs
NumPy and CuPy COS pricing.
Implement Fourier–COS pricing with a NumPy CPU path, then evaluate batched pricing with CuPy.
Bounded L-BFGS-B calibration.
Use bounded L-BFGS-B optimisation to estimate the Heston parameters from filtered market contracts.
Ten-feature neural surrogate.
Train a ten-feature PyTorch surrogate on a 600,000-sample synthetic design. Compare runtime and price-space error together rather than making speed the only objective.
03 / RESULTS
Results.
One retained run used 93 filtered out-of-the-money SPX contracts from 2014-06-02. CPU and GPU COS reached the same retained RMSE; the neural surrogate was faster but less accurate. This run was not independently reproduced for the website.
Context & limitations
The reported experiment uses a single SPX market snapshot. Broader market-regime generalisation and repeated benchmark reproducibility remain limitations. Restricted market data and model artifacts are not redistributed here.
Speech modelling and detection.
Speech technology / VAD + GMM