Traders call their position long skew if they bought an OTM put option and sold an OTM call option. You are moving towards expiration with a long skew position. What happens to the delta position of your long skew position?

The delta of your OTM put option will increase more towards 0, because it becomes less likely for the OTM put option to end up ITM. The delta of your OTM call option will decrease more towards 0, because it becomes less likely for the OTM call option to end up ITM. Since you are long the OTM put (which now increases in delta) and short the OTM call (which now decreases in delta), your overall delta position of a long skew position will increase if we get closer to maturity. Example: OTM put delta goes from -0.3 to 0, which is a change of +0.3. OTM call delta goes from 0.2 to 0, which is a change of -0.2. Together, since you are long the put and short the call, your delta change is equal to $1*0.3 - 1*-0.2 = +0.5$.

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Interview Questions Derivatives Theory Delta Change #1

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Delta Change #1

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