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Vanna Sign for Calls Depends on Whether the Option Is In or Out of the Money

Article Quant Q&A · Author: Stochastic vol
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Summary

The document examines how a call’s delta changes when implied volatility changes, a sensitivity known as vanna or DdeltaDvol. The questioner observes that higher volatility moves call delta toward the at-the-money level: this raises delta for an out-of-the-money call and lowers it for an in-the-money call. They use that reasoning to challenge a sign conclusion in an example from a dynamic hedging discussion.

The response points out a moneyness terminology error: an out-of-the-money call is above the underlying price, while a below-the-money call is in the money. This correction matters when assigning the positions in the example and determining the portfolio’s net vanna. The exchange does not provide the referenced graph, reproduce the original example, or independently confirm the full portfolio calculation, so its scope is limited to clarifying the call moneyness distinction.

Key ideas

  • A call’s delta tends toward the at-the-money delta as volatility rises.
  • This movement raises delta for out-of-the-money calls and lowers it for in-the-money calls.
  • An out-of-the-money call has a strike above the underlying price.
  • The terminology correction alone does not establish the net vanna of the full example.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Is Nassim Taleb wrong about his DdeltaDvol dynamics in his Dynamic Hedging book?


# Is Nassim Taleb wrong about his DdeltaDvol dynamics in his Dynamic Hedging book?












if you're long OTM calls, an increase in vol would increase your delta (converges to ATM) and if you're long ITM calls, increase in vol would decrease your delta (converges to ATM as well). So OTM calls have positive DdeltaDvol (Vanna) and ITM calls have negative Vannas. Following Nassim's example, if you're short OTM (below the money) calls and long ITM (above the money call) the book must have positive DdeltaDvol and not negative.

This is a Vanna graph from Natenberg's book to present a visual of the above. Can anyone please confirm this?

## Answer by user67097 (score 1)

https://quant.stackexchange.com/a/75269

You’ve probably figured this out by now. But you’re confusing OTM calls with below the money calls. An OTM call is above the money, not below.

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.