A new lattice approach for risk-minimization hedging under generalized autoregressive conditional heteroskedasticity models
Bibliographic record
Abstract
This paper explores the calculation of risk-minimization hedging strategies, specifically local and global risk minimization strategies for contingent claims under affine and non-affine GARCH models with the known closed forms of its first four moments across times under the physical measure. A unified and efficient willow tree method is introduced for various GARCH models. Unlike methods that provide option values and hedging ratios solely at the inception time, the proposed willow tree method generates a comprehensive table of option values and hedging ratios at each discrete time step across possible asset prices. Additionally, the method showcases robust performance in hedging at lower frequencies than the underlying asset’s modeling frequency (e.g., weekly or monthly hedging using a daily GARCH model). Lastly, the willow tree method outperforms the Monte Carlo method, offering greater efficiency, accuracy, and flexibility in solving risk-minimization hedging problems. • Propose a unified tree structure for GARCH models. • Efficiently and accurately compute quadratic risk-minimization for hedging European options. • Demonstrate robust performance at lower hedging frequencies.
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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 | 0.005 | 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 | 0.001 |
| 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 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".