EXPLICIT HESTON SOLUTIONS AND STOCHASTIC APPROXIMATION FOR PATH-DEPENDENT OPTION PRICING
Bibliographic record
Abstract
New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: (1) stochastic approximation replaces regression in the LSM algorithm; (2) explicit weak solutions to stochastic differential equations are developed and applied to Heston model simulation; and (3) importance sampling expands these explicit solutions. The approach complements Heston [(1993) A closed-form solutions for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies 6, 327–343] and Broadie & Kaya [(2006) Exact simulation of stochastic volatility and other affine jump diffusion processes, Operations Research 54 (2), 217–231] by handling the case of path-dependence in the option’s execution strategy. Numeric comparison against standard Monte Carlo methods demonstrates up to two orders of magnitude speed improvement. The general ideas will extend beyond the important Heston setting.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".