Hello, Suppose a stock is trading at 100, and the probability of a 90 put being in the money is 15% Then suppose the stock falls to 95. Does this mean the probability of an 85.5 put being in the money will also be calculated as 15%? The 95 put is 95% of the 100 selling price, and the 85.5 put is 95% of the 90 selling price. So they are both the same percentage distance away from the selling price of the stock. But the 85.5 put is a conditional probability... "given the stock declined by 10%, the 85.5 has an implied probability of being in the money of ..." I am basically wondering if the probability is mainly a function of distance, so everything will just shift linearly. Or does the option chain "know" the stock recently dropped, so the 85.5 put will have some other probability (like 25% or 10%, etc.). If the stock was dropping quickly, maybe 85.5 will receive a higher probability of being in the money, even though it has the same relative distance away as the 100/95 price put pairing. Or maybe since the price getting further below its recent trading range, the probability would be less.
Yes. Linear is your first, best assumption. But if the drop was event-driven, and any of the shock has not dispersed, then you will see the 15-delta be further from the money than the $5 from $100-->$95.... (And then there's *time*!!! If the shift *took*too*long* from $100-$95, that $85.50 may be *less* than a 15 delta. -- imagine it was expiration day, about 11am...... Yipes!)
Suppose the stock falls to 91 and you do your 90% calculation, does your theory still make sense ? Or does that answer your question ?
It is not linear. There are many factors to consider: Has the implied vol changed? Has realized vol changed? Time has most definitely changed, so how does that effect the 95% moneyness option? Has Skew changed? Options are convex, prices change as time, the underlying and volatility change.
As a general rule of thumb, look at the delta. If at 100, the put delta is .15, the probability is around 15%. If the stock then drops to 95 and the delta is now .25, the probability is now around 25%. I like to keep these references simple.
I agree with this, look at delta for a percentage. To further the delta example one could use gamma to find out the change in delta. Gamma is used to gauge how a one point move in the underlying will effect delta. This would be easy for a single point. So for multiple points you’ll have to use a gamma chart/software/calculator to figure these things out in more detail.
This is true over a short term. It will not help over a longer time period as time decay will also lower the delta over time if that strike is still OTM.
The probability of touching the strike price within the life time of the option is approximately twice the probability of finishing ITM.
beware of theta and vol changes, that might change the delta ... OP poster example is too simplistic but yes the delta is a good proxy to detemine the chance of getting in the money