Predictable Dynamics in the S&P 500 Index Options Implied Volatility Surface
Bibliographic record
Abstract
One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS).The usual approach consists of Þtting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data.However, recent empirical evidence suggests that the parameters characterizing the IVS change over time.In this paper we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice.We propose a two-stage approach to modeling and forecasting the S&P 500 index options IVS.In the Þrst stage we model the surface along the cross-sectional moneyness and time-to-maturity dimensions, similarly to Dumas et al. (1998).In the second-stage we model the dynamics of the cross-sectional Þrst-stage implied volatility surface coefficients by means of vector autoregression models.We Þnd that not only the S&P 500 implied volatility surface can be successfully modeled, but also that its movements over time are highly predictable in a statistical sense.We then examine the economic signiÞcance of this statistical predictability with mixed Þndings.Whereas proÞtable delta-hedged positions can be set up that exploit the dynamics captured by the model under moderate transaction costs and when trading rules are selective in terms of expected gains from the trades, most of this proÞtability disappears when we increase the level of transaction costs and trade multiple contracts off wide segments of the IVS.This suggests that predictability of the time-varying S&P 500 implied volatility surface may be not inconsistent with market efficiency.
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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 | 0.001 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".