Pricing options in a Markov regime switching model with a random acceleration for the volatility
Bibliographic record
Abstract
This article discusses option pricing in a Markov regime-switching model with a random acceleration for the volatility. A key feature of the model is that the volatility of the underlying risky security is randomly accelerated by a coefficient which is modulated by a continuous-time, finite-state Markov chain. Consequently, the degree of acceleration in volatility depends on the state of an economy represented by the state of the chain. A system of coupled partial differential equations for the prices of a standard European option over different economic states is derived. Using the homotopy analysis method originating from algebraic topology, a pricing formula for a standard European option is derived in the form of an infinite series. In addition, we give convergence conditions and compute implied volatilities using Monte-Carlo simulations. The implied volatilities can capture some important empirical features such as the implied volatility skew and smile for both VIX options and stock index options. We also provide numerical comparisons between call option prices from the first-order approximation of the proposed numerical method to those from the Monte-Carlo simulations.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".