I hear a back-of-the-envelope percentage guess for an option winding up in the money is to look at the delta. True? Does the usefulness of this measure vary with longer-term options? I have a LEAPS put OTM with a delta of -5.30. That can't possibly mean the option as only about a 5 percent chance of falling ITM, can it? Does the fact that is is on a leveraged volatility product (UVXY) change it's (semi-)accuracy?
How predictive is Delta?
- Thread starter dcwriter2
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The back of the envelope is dirty but OK for short-dated. Dirtier as expiration lengthens because for longer-dated the carry function can be a bigger - larger (impact) factor in the pricing.
This generally opens a pandora's box, but for longer-dated volatility can have less importance than carry - depends how long.
This generally opens a pandora's box, but for longer-dated volatility can have less importance than carry - depends how long.
If you want to get technical you can look at the BS formula and just look at the D2 half to get a little more accuracy on LEAPs. Still have the dividend uncertainty risk though.
My understanding is that delta or N(d1) in the BSM is a decent approximation for probability of expiring in the money. N(d2) is what you really want. This guy gives a decent explanation:
"N is just the notation to say that we are calculating the probability under normal distribution.
D2 is the probability that the option will expire in the money i.e. spot above strike for a call. N(D2) gives the expected value (i.e. probability adjusted value) of having to pay out the strike price for a call.
D1 (delta) is a conditional probability. A gain for the call buyer occurs on two factors occurring at maturity. One, the spot has to be above strike price. (Direction). Two, the difference between spot and strike prices at maturity (Quantum). Imagine, a call at strike price $100. If the spot price of the stock is $101 or $150, the first condition is satisfied. The second condition is about whether the gain is $1 or $50. The term D1 combines these two into a conditional probability that if the spot at maturity is above, what will be its expected value in relation to current spot price."
Formulas:
N(d1) and N(d2) are probability factors: N is the cumulative standard normal distribution function,
"N is just the notation to say that we are calculating the probability under normal distribution.
D2 is the probability that the option will expire in the money i.e. spot above strike for a call. N(D2) gives the expected value (i.e. probability adjusted value) of having to pay out the strike price for a call.
D1 (delta) is a conditional probability. A gain for the call buyer occurs on two factors occurring at maturity. One, the spot has to be above strike price. (Direction). Two, the difference between spot and strike prices at maturity (Quantum). Imagine, a call at strike price $100. If the spot price of the stock is $101 or $150, the first condition is satisfied. The second condition is about whether the gain is $1 or $50. The term D1 combines these two into a conditional probability that if the spot at maturity is above, what will be its expected value in relation to current spot price."
Formulas:
N(d1) and N(d2) are probability factors: N is the cumulative standard normal distribution function,
d2 = −log(X/S) − (r − 1 2σ2)τ σ √τ
d1 = d2 + σ √τ
Oh boy, oh boy! That's all totally wrong, man! Believe me!
What you need is "p0" --> study this code: https://www.elitetrader.com/et/thre...tion-pricing-model.350048/page-2#post-5203094
The probability for ITM for CALL is N(z0), and for PUT it's 1 - N(z0), ie.
pCALL_ITM = N(z0)
pPUT_ITM = 1.0 - pCALL_ITM
You're kind of embarrassing yourself. If you take this post down while you have time I'll take mine down and no-one will know you posted it. Hint, what is your N(z0) in terms of D1 and D2 in BS? If that isn't working, maybe write out the parameters of N(z0) in terms of each of the parameters of BS, then explain how it's different from D1? Then explain why D1 is more appropriate than D2?
No, man, read on...
Boy, it's clear and openly shown in the above code and even extensively explained
in the subsequent posting https://www.elitetrader.com/et/thre...tion-pricing-model.350048/page-2#post-5203373
z0 is the midpoint between z2 and z1 (in original BSM z1 is called d1 and z2 is called d2).
If you still have any further questions, so let me know...
See also this, especially for the said "p0" for/in BSM:
https://www.elitetrader.com/et/threads/the-fairput-initiative.349291/page-13#post-5193421
You mean the thread where everyone is letting you know that you're embarrassing yourself? Sorry, I wasn't aware of it or I wouldn't have posted repeating what they've already told you.No, man, read on...
Boy, it's clear and openly shown in the above code and even extensively explained
in the subsequent posting https://www.elitetrader.com/et/thre...tion-pricing-model.350048/page-2#post-5203373
z0 is the midpoint between z2 and z1 (in original BSM z1 is called d1 and z2 is called d2).
If you still have any further questions, so let me know...
See also this, especially for the said "p0" for/in BSM:
https://www.elitetrader.com/et/threads/the-fairput-initiative.349291/page-13#post-5193421