A Binomial Option Pricing Model under Stochastic Volatility and Jump
Bibliographic record
Abstract
Abstract Numerous papers have investigated the pricing of options on traded assets when either the underlying asset follows a jump diffusion process or the volatility of the underlying asset is assumed to be stochastic. This paper extends the literature by combining the transformation technique of Hilliard and Schwartz (1996) and the discrete‐time jump diffusion model of Amin (1993) to develop a simple tree. The advantage of this approach is that it can easily value American options under a stochastic volatility and jump environment. We investigate how stochastic volatility and jump parameters affect the option values. From the simulation results, we find that the jump parameters significantly affect the American and European option values, especially for the near atthe‐money options. We also demonstrate that our model can capture the volatility smile observed in the market. Résumé Nombre d'articles ont examiné la fixation du prix des options lorsque que le sous‐jacent suit un processus de diffusion avec sauts ou que la volatilité du sous‐jacent est présumé stochastique. Notre article pousse plus loin ces études en combinant la technique de transformation de Hilliard et Schwartz (1996) et le modèle de la diffusion avec sauts du temps discret d'Amin (1993) pour développer un schéma simple. L'avantage de notre approche est de permettre une évaluation facile des options américaines lors d'une volatilité stochastique ou dans un environnement avec sauts. Nous examinons comment la volatilité stochastique et les paramètres avec sauts affectent les valeurs des options. Grâce à des résultats simulés, nous trouvons que les paramètres avec sauts affectent considérablement les valeurs de types américain et européen, en particulier pour l'option à la parité proche. Nous démontrons également que notre modèle pourra décrire le phénomène du ‘volatility smile’ observé au marché.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".