pevece
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| Total Posts: 6 |
| Joined: Jul 2021 |
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Hello people, can anyone help me understand the question below?
Question:
If a stock price is currently at 100$, what is the probability of the stock touching 85$(The 85$ is currently at a delta of 0.27 with the stock currently at 100$)?
The answer to the question is 2*0.27=0.54 with the assumption that the probability of touch is approximate twice the delta.
Restrictions:
However, a restriction is added to reduce the probability of the event happening: The stock can’t touch the 115$ price or above first before touching the 85$.
The 115$ is also at a delta of 0.27 with the stock currently at 100$. After 85$ is touched the stock can now touch any other price with no restriction.
So simply put the stock can touch any price below 115$. But before it can touch the 115$ price or above, it must have touched the 85$ price first.
Please can you help me with this question using probability? Thanks for your contributions in advance. |
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nikol
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| Total Posts: 1457 |
| Joined: Jun 2005 |
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| First hint: you forgot to mention maturity ot any kind of horizon, like number of steps (i see minimum 2), because you put some conditions here. |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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pevece
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| Total Posts: 6 |
| Joined: Jul 2021 |
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Maturity can be of any value. Let's say with 30 days to expiration, stock XYZ is currently trading at $100, Its $115 strike call has a delta of 0.27 and its $85 strike put has a delta of 0.27.
As for conditions, it is one actually. The probability that the stock would touch $90. But you know the stock theoretically can rise to as much as $900 or more before going down to touch the $90. So, my condition is strictly limiting the rise to <$115 before touching 90$. After the $90 price is touched nothing else matters about the stock path.
So by that approximate formula: the probability of touching $90 is 2*0.27=0.54
But if the condition is added that the $115 price can not be touched first before $90, I think the probability should be less than 0.54.
I don't know if my reply made the question clear? |
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nikol
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| Total Posts: 1457 |
| Joined: Jun 2005 |
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Second hint/question:
"assumption that the probability of touch is approximate twice the delta"
How can you get down-touch probability at 54%? It would then mean that up-touch probability is also 54%, right? Does it imply 108% total probability? How can that be?
Something is wrong here.
I presume, we are within Black-Scholes framework.
This condition is 2-steps."The stock can’t touch the 115$ price or above first before touching the 85$".
By the way, down-barrier = 85$ or 90$ ?? |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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pevece
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| Total Posts: 6 |
| Joined: Jul 2021 |
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Yes, my mistake the down barrier is 85, not 90.
Yes actually you're right it is indeed a second condition.
So since my assumption is wrong, how can I solve it instead? |
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nikol
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| Total Posts: 1457 |
| Joined: Jun 2005 |
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I didn't solved it, even didn't look into solution. I just help you to formulate the problem so you can do it yourself.
Try 1,2 step binomial model, plug-in your touch probabilities, derive deltas and use them too. It will help you to calibrate up/down probabilities and you will get an answer. |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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pevece
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| Total Posts: 6 |
| Joined: Jul 2021 |
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| I would do that. Thank you. @nikol |
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nikol
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| Total Posts: 1457 |
| Joined: Jun 2005 |
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| Put an answer here. I m curious. Others might be too. |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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