Markov-Modulated and Shifted Wishart Processes with Applications in Derivatives Pricing
Bibliographic record
Abstract
The popular Wishart (WI) processes, first introduced by Bru in 1991, exhibit convenient analytical properties for modeling asset prices, particularly a closed-form characteristic function, and the ability to jointly model stochastic volatility and correlation. These features tend to increase substantially during crisis periods, more than predicted by a Wishart dynamic. Moreover, the variance processes implied by the Wishart, similar to CIR models, have no buffer away from zero. In this paper, we introduced the Markov-Modulated Shifted Wishart processes (MMSW) and the embedded Shifted Wishart processes (SW) to address these shortcomings in the modeling of asset prices. We obtain analytical representations for several characteristic functions. We also estimate the parameters and evaluate the price of Spread options via the Fourier transform under the two new models compared to the standard Wishart. Our analyses demonstrate a significant impact of the MMSW process compared to the standard Wishart process of up to 7% in Spread option prices.
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.
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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".