Mispricing of S&P 500 Index Options
Bibliographic record
Abstract
We document widespread violations of stochastic dominance by one-month S&P 500 index call options market over 1986-2006. These violations imply that a trader can improve her expected utility by engaging in a zero-net-cost trade. We allow the market to be incomplete and also imperfect by introducing transaction costs and bid-ask spreads. Even though pre-crash option prices conform to the Black-Scholes-Merton model reasonably well, they are incorrectly priced if the distribution of the index return is estimated from time-series data even with a variety of statistical adjustments. Even though there are fewer violations by OTM calls than by ITM calls, there are still substantial violations by OTM calls, contradicting the inference drawn from the observed implied volatility smile that the problem primarily lies with the left-hand tail of the index return distribution. Most of the violations by post-crash options are not due to the smile being too steep: options are underpriced over 1988-1995 and overpriced over 1997-2006. The decrease in violations over the post-crash period 1988-1995 is followed by a substantial increase in violations over 1997-2006. These results do not support the hypothesis that the options market is becoming more rational over time. Current draft: November 10, 2006 JEL classification: G13 Keywords: Derivative pricing; volatility smile, incomplete markets, transaction costs; index options; stochastic dominance bounds We thank workshop participants at the German Finance Society Meetings 2004, the Bachelier 2004 Congress, the EFA 2005 Meetings, the Frontiers of Finance conference 2006, the Alberta/Calgary 2006 conference, the Universities of Chicago, Iowa, Southern California, Maryland, Texas-Austin, Torino, Utah and Concordia, Laval, New York, Princeton and St. Gallen Universities and, in particular, Yacine Ait-Sahalia, David Bates, Duke Bristow, Larry Harris, Steve Heston, Jim Hodder, Mark Loewenstein, Matthew Richardson, Jeffrey Russell, Hersh Shefrin and Greg Willard for their insightful comments and constructive criticism. We also thank Michal Czerwonko for excellent research assistance. We remain responsible for errors and omissions. Constantinides acknowledges financial support from the Center for Research in Security Prices of the University of Chicago and Perrakis from the Social Sciences and Humanities Research Council of Canada. E-mail addresses: gmc@ChicagoGSB.edu, Jens.Jackwerth@uni-konstanz.de, SPerrakis@jmsb.concordia.ca.
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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 | 0.020 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 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".