# Larger negative delta and larger positive delta

Book : Natenberg: Option Volatility and Pricing

Chapter : Risk Measurement I Topic : Interpreting the Risk Measures, page 115

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

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.

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.

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