Numerical Pricing of Contingent Claims on Multiple Assets and/or Factors - A Low-Discrepancy Markov Chain Approach
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Bibliographic record
Abstract
We develop a Markov chain pricing method capable of handling several state variables. The Markov chain construction of Duan and Simonato (2000) is modified so that higher-dimensional valuation problems can be dealt with. Their design relies on a Cartesian product, which grows in a power fashion as the number of assets/factors increases. We use a multi-dimensional lowdiscrepancy sequence as the building block for constructing the Markov chain in order to take advantage of the high degree of uniformity inherent in such sequences. Our design contains two critical components. First, we have devised a way of computing analytically the entries of the transition probability matrix and then shown that such a Markov chain converges weakly to the target Markov process. Second, we have utilized an elliptical restriction as a way of removing non-critical components of the Markov chain to enhance the computational efficiency. Numerical examples are provided.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
| 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