Efficient calibration of the shifted square-root diffusion model to credit default swap spreads using asymptotic approximations
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Bibliographic record
Abstract
We derive a closed-form approximation for the credit default swap (CDS) spread in the two-dimensional shifted square-root diffusion (SSRD) model for its efficient calibration, using asymptotic coefficient expansion technique to approximate solutions of nonlinear partial differential equations. Specifically, we identify the Cauchy problems associated with two terms in the CDS spread formula that lack analytical solutions and derive asymptotic approximations for these terms. Our approximation does not require the assumption of uncorrelated interest rate and default intensity processes as typically required for calibration in the SSRD model. Through several numerical experiments using market data on CDS spreads, we demonstrate the accuracy and efficiency of our proposed formula when calibrating the SSRD model.
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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 | 0.000 | 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 | 0.001 | 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.
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