Abstract. The Dimopoulos Chain is a Markov model over nine states, formed by crossing terciles of options-dealer gamma with terciles of realized volatility, forecasting volatility one day ahead. Out of sample its states add information beyond the VIX and beyond GARCH(1,1), miss the hurdle against HAR, and add nothing once the asymmetric GJR-GARCH model of Glosten, Jagannathan and Runkle (1993) enters the baseline. Verdict: PARTIAL; the name is not earned at the strictest bar.
1. Introduction
Black-Scholes prices every option with one constant volatility; markets do not behave that way. Volatility arrives in regimes, and one structural driver is the positioning of options dealers. When dealers are long gamma their hedging pins the market; when they are short gamma the same hedging amplifies every move. BlueShip, the pipeline behind this site, had already validated that signal against the VIX at t = 7.4. This paper asks whether it beats the econometric benchmarks.
2. Model and data
The chain’s nine states are the interaction of a gamma tercile with a realized-volatility tercile; the distribution conditional on today’s state is the forecast for tomorrow. A name is earned here by surviving the pipeline’s hurdles; a model that fails is kept as an exhibit under its own name.
3. Results
Table 1 sets the states against progressively stricter baselines: they clear the VIX and GARCH(1,1), fall below the hurdle against HAR, and add nothing against the combined stack.
| Chain states add information beyond… | NW t | Outcome |
|---|---|---|
| VIX (implied forecast) | 4.34 | PASS |
| GARCH(1,1) | 3.19 | PASS |
| HAR (workhorse for realized vol) | 2.03 | below gate |
| HAR + VIX + GJR-GARCH combined | 1.02 | FAIL |
GJR-GARCH is the best forecaster in the stack and the one that closes the door. Its leverage effect, down moves raising volatility more than up moves, is plausibly a reduced form of the dealer mechanism: a fall induces put buying, which pushes dealers short gamma, which amplifies volatility. An econometric model 33 years old already captured indirectly what the chain measures directly.
4. Findings that survive
Two results hold whatever the ranking (Table 2). The econometric stack beats the forecast implied by option prices by a wide margin. Options nonetheless trade against implied volatility, which no model sets, and the gap is the variance risk premium. The state map locates the danger: one state of nine is where short-volatility strategies fail, and it is identifiable a day in advance. Timing that gap is the live research programme.
| Claim | What the record says |
|---|---|
| Evaluation | out of sample, refit monthly, no look-ahead, so no forecast uses later information |
| Beats the implied forecast | GJR, HAR and every chain-augmented combination, by a wide and significant margin |
| Does not beat it | the chain’s raw state-conditional means alone |
| Implied variance minus realized, by state | positive in 8 of 9 states |
| Hit rate where dealers are pinned | up to 90% |
| The exception | exactly 1 state of 9: dealers exposed, volatility already high, implied variance below realized |
| Version | Baseline it faced | NW t | Outcome |
|---|---|---|---|
| 1 (this paper) | HAR + VIX + GJR-GARCH | 1.02 | PARTIAL, not promoted |
| 1.1 | HAR + VIX + plain GARCH | 2.83 | cleared |
| 1.1 | the same, augmented with GJR | 1.02 | retired |
| 1.5 | linear emissions (the equations mapping each state to a forecast) replaced by a neural network | −4.37 | retired, forecast worse not better |
| 3 | shrunk state corrections on term structure and event arrivals, over a log HAR + VIX + GJR backbone (separate paper) | below gate | retired |
References
- Black, F., and Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637–654.
- Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307–327.
- Corsi, F. (2009). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7(2), 174–196.
- Glosten, L. R., Jagannathan, R., and Runkle, D. E. (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance, 48(5), 1779–1801.