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Put Delta Changes from Spot, Volatility, and Time Decay

Article Quant Q&A · Author: Sumit
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Summary

The document investigates why a short put’s hedge delta increased even as the underlying price rose slightly. It reports that volatility also declined and two days elapsed, with a long time remaining to expiration. The response identifies charm, or delta decay, as a possible explanation alongside the more familiar delta, gamma, and vega effects.

The intuition offered is that an in-the-money put’s delta tends toward its expiration behavior as time passes, while lower volatility can also raise the put delta in the described setting. These forces may outweigh the opposing effect of a higher spot price. The answer is explicitly a qualitative guess rather than a worked calculation, and it recommends testing the inputs in a Black–Scholes formula. It does not establish which factor dominates numerically.

Key ideas

  • An option’s delta can change through spot, volatility, and time passage.
  • Charm describes the sensitivity of delta to the passage of time.
  • For the reported in-the-money put, declining volatility and elapsed time may raise delta despite a higher spot price.
  • The response offers intuition but no numerical decomposition of the observed hedge change.

Tags

OptionsDerivatives pricingVolatilityRisk management
Full text
# Why my delta position is increasing with increase in spot?


# Why my delta position is increasing with increase in spot?












I am trying to take position in future as per the delta position of short put. My strike is 13794 for short put option, spot 10305.3 and volatility is 20.153 then I am getting 5890 position to buy and delta of 0.7222. Now when my spot increased to 10311.2 for same strike and volatility changed to 20.03, I am getting 5906 position to buy and delta of 0.724. Why the delta position is telling me to buy more even with increase in spot price? Is it because of the volatility because time to expiry is 790 days and these spot prices are 2 days apart.

## Answer by David Duarte (score 3)

https://quant.stackexchange.com/a/55346

Without doing any calcs, I would guess it's because of the 2 days passed and the decrease in vol.

Besides the more commonly known greeks (delta, gamma, vega), you have some other interesting second order greeks and the one that will explain what you are observing is probably the delta decay (Charm).

Intuitively think of it like this: your put is in the money so it will naturally tend to a delta of 1 as time passes. Also, in the extreme case of the vol going to zero, it would be as if you were at maturity because there is no optionality so a decrease in vol in this case would increase your delta.

You do however, have a factor that would make the delta decrease: the spot went up. But I'm guessing the other 2 make up for that.

Play with these inputs using a simple Black Scholes formula.

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.