How a Put Spread’s Delta and Gamma Change as Spot Falls

Summary

The document raises a question about the changing delta and gamma of a long higher-strike put combined with a short lower-strike put as the underlying price falls. The author reasons that both puts eventually become in the money, while the higher-strike put remains further in the money and has the larger absolute delta. On that basis, the author expects the net position delta to remain negative and approach zero, and questions a book’s description of the spread’s delta profile and related hedge direction.

This is a question rather than a resolved analysis: it provides no reply, pricing assumptions, volatility or time-to-expiry conditions, or numerical example. Its useful contribution is to identify a distinction between the position’s net delta and its changing gamma, and to show why option spread Greeks should be checked across underlying prices before drawing hedging conclusions. The claim about delta is not established for all possible model assumptions or market conditions.

Key ideas

• The position combines a long higher-strike put with a short lower-strike put.
• The author expects net delta to stay negative as spot falls because the higher-strike put has greater absolute delta.
• The document questions whether net gamma can change sign while net delta remains negative.
• No answer or numerical analysis is provided, so the stated delta conclusion remains unverified.

Tags

# Net delta and gamma profile of a put spread


# Net delta and gamma profile of a put spread












I have a question regarding the description in Simon Gleadall's book -- option gamma trading which you can find a copy HERE. The following paragraph he discussed about gamma and delta profile of a long 95/short 90 put spread in a falling market.

I think he's correct about the net gamma of the PS changing from positive to negative, however I think his interpretation of net delta is incorrect. In a falling market, say spot falling from 100 to 0, both the 95put and 90put eventually become ITM options, but 95put would always be more ITM than 90put. We know that the more ITM an option is, the more its delta (absolute value) gets closer to 1. Long 95put would produce a negative delta, and the absolute value of its delta is always greater than that of the short 90put. Therefore, the net delta profile of the long 95put/short 90put is always negative. The net delta would get closer and closer to 0, but it could never become long delta overall.

I need to get this question resolve before I continue reading the book, because the author spend a few more paragraphs talk about hedging such portfolio. If the direction of net delta is not even correct, then the corresponding hedging direction would not make sense either.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.