How Volatility Changes the Delta of Calls

Summary

This note explains why an increase in volatility can raise the delta of an out-of-the-money call while lowering the delta of an in-the-money call. It frames the effect through the option’s asymmetric payoff: an out-of-the-money call pays nothing in many outcomes, while an in-the-money call already has a greater chance of finishing with value. Greater volatility spreads the possible underlying prices, changing the likelihood of those outcomes and moving the deltas toward the middle of their range.

The explanation is qualitative and gives no formula, model assumptions, or numerical example. It describes how volatility affects delta while holding other factors conceptually fixed; it does not imply that either delta changes because the underlying itself must move. The account is an intuition for the relationship, rather than a full derivation, and does not discuss how the effect varies across maturities, pricing models, or market conditions.

Key ideas

• Higher volatility can increase an out-of-the-money call’s delta by raising the likelihood of a positive payoff.
• Higher volatility can decrease an in-the-money call’s delta by increasing the likelihood that it finishes without value.
• These effects move call deltas toward the middle of their range.
• The explanation is qualitative and does not provide a model-based derivation.

Tags

# Effect of volatility on the delta of a call option


# Effect of volatility on the delta of a call option












In the book 'Dynamic Hedging', Nassim Taleb writes:

```
    All operators in options learn that a rise in 
volatility would cause the delta of an out of the money
 call to rise and that of an in the money call to drop,
thereby bringing deltas closer to 50%.
```

Why is this? Why would the OTM delta rise? It can only rise if the underlying rallies. But if underlying rallies, the ITM delta will also rise, approaching 1. Why would it drop?

## Answer by emcor (score 11, accepted)

https://quant.stackexchange.com/a/18064

Options have an asymmetric payoff profile: The payoffs are zero for almost all cases and positive else (as we well know).

If the option is OTM, most of its payoffs are zero. A rise in volatility will hence increase the likelihood for instead positive payoffs from a change in the underlying price (i.e. delta increases).

If the option is already ITM, most(many) of its payoffs are already positive. Hence an increase in volatility will increase the likelihood for zero payoffs instead from a shift in the underlying price (i.e. delta decreases).

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.