Options Gamma Spreads Across Correlated Assets: Hedging and Model Risk
Summary
The document considers a proposed options relative-value trade: buy gamma on one underlying and sell gamma on a correlated underlying whose same-moneyness call has higher implied volatility. It describes the setup using a return beta, an implied-volatility difference, and high regression fit, then asks whether those features support a zero-cost position.
The accepted response recommends focusing on portfolio exposures rather than forcing zero initial cost. It suggests hedging vega against broad implied-volatility moves, neutralizing delta with the underlying, and potentially adding options to control gamma exposure. The discussion offers no backtest or empirical performance evidence; it only assesses the idea conceptually. A second response cautions that a spread between implied and realized volatility can still lose money and argues that a model of their relationship is needed. Correlation and beta alone do not establish that the volatility difference is mispriced, and transaction costs may prevent a seemingly attractive trade from being profitable.
Key ideas
- A zero-cost constraint can force an unbalanced options position and may be a poor design objective.
- Delta and broad volatility exposure can be hedged with stock and additional options.
- High correlation between underlyings does not by itself show that their implied-volatility difference is exploitable.
- A model linking realized and implied volatility is needed to assess the trade.
- The discussion provides conceptual cautions rather than measured trading results.
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Full text
# Beta vs. Implied Volatility statistical arbitrage using options
# Beta vs. Implied Volatility statistical arbitrage using options
Let two underlyings, $S_{1}$ and $S_{2}$, are correlated and $\beta$ is the slope of their returns linear regression, that is, it says how much $S_{1}$ co-variates with $S_{2}$ variance.
For instance, let
$$\beta=\dfrac{\sigma_{S_{1}S_{2}}}{\sigma^{2}_{S_{2}}}=0.83$$
that is, when $S_{2}$ raises by $1\%$ $S_{1}$ goes up by $0.83\%$; in this example we can assume to know the true value of $\beta$, then no estimation error is present.
Now consider two Call options: the former, $c_{1}$, is written on $S_{1}$ and the latter, $c_{2}$, is written on $S_{2}$, and they have both the same moneyness (e.g. 102%).
According to BMS formula, the implied volatility, $v_{1}$, extrapolated from $c_{1}$ is greater than the one, $v_{2}$, extrapolated from $c_{2}$.
For instance, let
$$v_{1}-v_{2}=6\%$$
on annual basis.
$S_{1}$ and $S_{2}$ are strongly correlated and their linear regression $R^{2}$ is above $0.8\approx0.9$.
What about buying $S_{2}$ Gamma selling $S_{1}$ Gamma in order to get a zero cost position but having sold (bought) an implied volatility greater (smaller) than realized volatility?
## Answer by jordi (score 6, accepted)
https://quant.stackexchange.com/a/8380
This is definitely a valid (and possibly viable) strategy.
I think that your constraint of zero costs is a red herring and serves no useful purpose beside forcing you to take lopsided bets in the direction of the cheaper option. I would try instead to build a portfolio that has zero vega (hedged against overall moves in market-wide implied volatility) and zero delta (accomplished by overlaying a stock position). If possible may be able to combine additional options in your portfolio (i.e., more than two) to shield yourself against gamma exposure.
I am quite sure that other players in the market are doing this, so my guess is that this strategy, if well-diversified, could make good money before costs, but would be likely a non-trivial task to make it profitable after costs (as with most things in finance).
## Answer by user2183336 (score 3)
https://quant.stackexchange.com/a/8378
You could sell a high realized volatility against a low implied all day and bust out in a month. Doing this as a inter-stock spread isn't going to make it much of a better trade. If you want to take advantage of realized vol vs. implied vol you need a model that describes the relationship between the two.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.