On the Interest Rate Derivatives Pricing with Discrete Probability Distribution and Calibration with Genetic Algorithm
Bibliographic record
Abstract
Bond prices and fixed-income derivatives intricately depend on the ever-evolving landscape of interest rates. This study introduces an exceptionally efficient semi-analytical pricing methodology designed for discretely updated path-dependent interest rate options. Our approach involves the derivation of an analytical solution for the characteristic function of the logarithm of the discretely discounted strike price, enabling the computation of coefficients for the Fourier-cosine series governing the path-dependent option pricing. The distinctive feature of our pricing method lies in the utilization of a modified Skellam probability distribution to model interest rate increments, resulting in a remarkably swift and precise calculation process. Unlike existing solutions for similar pricing challenges, our proposed formula considerably enhances computational efficiency. Moreover, we delve into the influence of central bank monetary decision probabilities on option prices via a comprehensive series of numerical experiments. In an effort to further fine-tune the calibration parameter values for the yield curve, we employ a genetic algorithm, thus contributing to the heightened precision of our pricing model. This research, with its innovative approach, not only refines pricing procedures but also offers valuable insights into the dynamic interplay between monetary policies and fixed-income derivatives.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".