How Stock Splits Affect Option Greeks

Summary

The document asks whether option Greeks should be adjusted after a stock split. Its key distinction is between changes caused mechanically by the split and changes caused by market reactions. Since a split changes the share-price scale while leaving market capitalization unchanged, traders may behave similarly, but the units used to express Greeks also change. Gamma is measured per dollar of underlying price, and vega is measured per unit of volatility, so raw Greek values can change with the split even when the economic exposure is comparable.

The answer adds that implied volatility and Greeks may also shift because of reactions to the corporate event. The suggestion that lower share prices attract new traders is posed as a hypothesis, not demonstrated evidence. The discussion is brief and does not provide a quantitative adjustment formula or empirical results; conclusions depend on how exposures are normalized and on assumptions about market behavior.

Key ideas

• A stock split changes the price scale, which can change the numerical values of option Greeks.
• Gamma and vega have units that affect how their raw values compare across a split.
• A split may also affect implied volatility and Greeks through market reactions.
• The idea that a lower share price attracts new traders is raised as a possibility, not established evidence.

Tags

# Greeks and splits


# Greeks and splits












Should we adjust greeks on stock splits? Let's just ask about splits instead of reverse splits. I'm also interested how answers change if we change models/assumptions.

I have some contradicting thoughts:

- We should not adjust, because market conditions are the same i.e. market cap stays the same, and we assume traders still act the same.

- Volatility increases which will affect greeks (at least the higher order derivatives taken w.r.t volatility). I think volatility increases because newer traders enter at the lower price point.

As I wrote this, I realized this may be a hidden "implied vs historical volatility" question, but I'm still interested in answers. Thanks!

## Answer by Quantoisseur (score 2)

https://quant.stackexchange.com/a/57289

Disregarding exogenous factors, the unit of Gamma is 1/$ and the unit of Vega is \$/sigma so the raw greek values will change in a stock split.

Including exogenous factors, you're right, implied volatility and the greeks could change from the reaction to the event.

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.