Bibliographic record
Abstract
The guaranteed minimum withdrawal benefit (GMWB) rider guarantees the return of premiums in the form of periodic withdrawals while allowing policyholders to participate fully in any market gains. The product has evolved into a lifetime version (GLWB) and is a vital component of the variable annuity marketplace, representing asset values of $294B as of September 2011. \n \nGMWB riders represent an embedded option on the account value with a fee structure that is different from typical financial derivatives. We present an in-depth study into pricing and hedging the GMWB rider from a financial economic perspective. Our main contributions are twofold. We construct a binomial asset pricing model for GMWBs under optimal policyholder behaviour which results in explicitly formulated perfect hedging strategies in a binomial world. The numerical toolbox for pricing GMWBs in a Black-Scholes world is expanded to include binomial methods. \n \nTo motivate our work, we begin with a review of the continuous model and a comprehensive synthesis of results from the literature. Throughout, particular focus is placed on the unique perspectives of the insurer and policyholder and the unifying relationship. We also present an approximation algorithm that significantly improves efficiency of the binomial model while retaining accuracy. Several numerical examples are provided which illustrate both the accuracy and the tractability of the model. \n \nFinally, we explore the effect of deterministic mortality on pricing GMWBs, and run mortality simulations to obtain hedging results which support the diversification principle.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".