Option pricing for jump diffussion model with random volatility
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Bibliographic record
Abstract
Purpose Option pricing based on Black‐Scholes model is typically obtained under the assumption that the volatility of the return is a constant. The purpose of this paper is to develop a new method for pricing derivatives under the jump diffusion model with random volatility by viewing the call price as an expected value of a truncated lognormal distribution. Design/methodology/approach Using Taylor series expansion the call price under random volatility is expressed as a function of kurtosis of the observed volatility process and applied to various class of GARCH models. Findings A modified option pricing formula is developed for jump diffusion process model with random volatility. Originality/value The main contribution of the paper is the development of a kurtosis‐dependent option pricing formula for a jump diffusion model with random volatility.
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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 | 0.001 |
| 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