04 / Systems / 2024–2025
Heston pricing and calibration.
Individual dissertation / Heston model
01 / SCOPE
Problem and
scope.
Repeated option pricing can make model calibration expensive. My dissertation compared a NumPy CPU path, batched GPU evaluation and a learned surrogate to measure the trade-off between runtime and price-space 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
Implement CPU and GPU pricing paths.
Implement Fourier–COS pricing with a NumPy CPU path, then evaluate batched pricing with CuPy.
Constrain the calibration parameters.
Use bounded L-BFGS-B optimisation to estimate the Heston parameters from filtered market contracts.
Train and evaluate an approximation.
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.
04 / SUMMARY
The surrogate reduced runtime in the retained run, but price error increased and the run was not independently reproduced.
Speech modelling and detection.
Speech technology / VAD + GMM