How Gamma Changes Delta as the Underlying Moves
Summary
The document explains how gamma shapes the change in an option position’s delta as the underlying price moves. With negative gamma, delta moves against the price change: a rising underlying makes the position’s delta more negative, while a falling underlying makes it more positive. For a position kept near delta neutral, these changes can increase the need to rebalance and are unfavorable when the market moves sharply. The discussion links this exposure to a preference for a stable or slowly moving market.
The responses contrast this with positive gamma, where delta moves in the same direction as the underlying, making large moves potentially beneficial. They define delta as sensitivity of option value to the underlying and gamma as sensitivity of delta to the underlying. The explanation is qualitative and depends on the position’s net gamma; it does not give a specific options structure, numerical example, or hedging procedure. The central lesson is to interpret delta changes together with gamma rather than treating delta as fixed.
Key ideas
- Gamma measures how an option position’s delta changes as the underlying price moves.
- With negative gamma, a price rise makes delta more negative, while a price fall makes it more positive.
- A negative gamma position generally benefits from a stable market or slow price changes.
- A positive gamma position can benefit from large, rapid underlying moves.
- The direction and size of the effect depend on the position’s net gamma.
Tags
Full text
# Larger negative delta and larger positive delta
# Larger negative delta and larger positive delta
Book : Natenberg: Option Volatility and Pricing
Chapter : Risk Measurement I Topic : Interpreting the Risk Measures, page 115
Link: link
As the market falls, the delta becomes a larger positive number. For the same reason we do not want the stock price to rise (we are creating a larger negative delta in a rising market), we also do not want the stock price to fall (we are creating a larger positive delta in a falling market). If we do not want the market to rise and we do not want the market to fall, there is only one favorable outcome remaining: we must want the market to sit still. In fact, a negative gamma position is a good indication that a trader either wants the underlying market to sit still or move only very slowly. A positive gamma position indicates a desire for very large and swift moves in the underlying market.
Question : What is meaning of, we are creating a larger negative delta in a rising market
we are creating a larger positive delta in a falling market
## Answer by Valter (score 0)
https://quant.stackexchange.com/a/77703
It is important to understand the concept of Delta and Gamma. Delta is the change in the value of an option given the change in the underlying price, $\frac{dC}{dS}$. And Gamma is the change of Delta with respect to change in the underlying price, $\frac{d^2C}{dS^2}$. Intuitively, for a position with positive Delta and Gamma, if the underlying price increases, Delta increases relative to Gamma. Thus, "creating" a larger positive Delta in a rising market. Same goes for a falling market.
That is the basic intuition. From here, you can apply the idea to any type of option position.
## Answer by user name (score 0)
https://quant.stackexchange.com/a/80551
The book infers that the gamma considered is negative. Recall that gamma is the derivative of delta w.r.t. the underlying price. Hence, if the price increases, the delta will fall, and vice versa.
I think the author uses 'we create a larger negative delta' because in this context, our goal is to maintain a delta-neutral portfolio (delta close to 0), and 'creation' of both negative and positive deltas in large magnitudes would be unfavorable.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.