Estimating Short Strangle One-Sided Touch Probability

Summary

The document gives an approximation for the probability that a stock touches a short strangle’s higher strike without touching its lower strike. It defines events for touching each side and expresses the desired probability as the probability of touching the higher strike minus the probability of touching both strikes. The cited approach estimates each one-sided touch probability as twice the probability that the expiry price lies beyond that strike, then approximates the joint touch probability by multiplying the two one-sided probabilities.

The question assumes a symmetric random walk and gives equal deltas for the call and put, but the response does not work through a numerical result. The approximation depends on the stated touch and joint probability assumptions; the document offers no validation or discussion of how accuracy changes with market dynamics, strike placement, or expiry. It is best read as a rough probability decomposition, not a precise model for all strangles.

Key ideas

• The probability of touching only the higher strike equals its touch probability minus the probability of touching both strikes.
• The proposed method estimates a one-sided touch probability from the terminal probability beyond that strike.
• It approximates the probability of touching both sides as the product of the separate touch probabilities.
• The result is an approximation under a symmetric random walk assumption, with no accuracy analysis provided.

Tags

# Probability of touching short call strike and not touching touching short put strike of a short strangle?


# Probability of touching short call strike and not touching touching short put strike of a short strangle?












I just came across a blog post. I believe the answer is a correct approximation:

http://tastytradenetwork.squarespace.com/tt/blog/probability-of-touching-both-sides

I modified the question in the post to: What is the combined probability of the stock moving up to touch the short call strike but not touching the short put strike price of the short strangle?

**Same delta values of 0.3 for the call and 0.3 for the put. Assume symmetric random walk.

## Answer by ir7 (score 2, accepted)

https://quant.stackexchange.com/a/65453

If $A$ is the event of touching the higher strike (between now and expiry) and $B$ is the event of touching the lower strike (and $B^c$ is its complement, that is the event of not touching the lower strike), then:

$$P(A\cap B^c) = P(A) - P(A\cap B). $$

They have already estimated POT on the higher (lower) side, $P(A)$ ($P(B)$), to be twice the probability of stock price at expiry to be less than the higher/lower strike, and POT on both sides, $P(A\cap B)\approx P(A)\cdot P(B)$.)

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.