Simulating from the Heston model: A gamma approximation scheme
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract The Heston model is appealing as it possesses a stochastic volatility term as well as semi-closed formulas for pricing European options. Unfortunately, few simulation schemes for this model can handle the violation of the Feller Condition. An algorithm based on the exact scheme of Broadie and Kaya to simulate price paths under the Heston model is introduced. In order to increase the speed of their exact method, we use a gamma approximation. According to Stewart, Strijbosch, Moors and Batenburg, it is possible to approximate a complex gamma convolution (similar to the representation given by Glasserman and Kim) by a simple moment-matched gamma distribution. We also perform a review of popular simulation schemes for the Heston model and validate our approach through a simulation study. The gamma approximation scheme appears to yield small biases on European and Asian option prices when compared to the most popular schemes.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it