Delta = probability of excercise?

tickersu wrote:
http://www.optionsplaybook.com/options-introduction/option-greeks/
http://money.stackexchange.com/ques...nify-the-probability-of-expiring-in-the-money
Delta isn’t a probability, but apparently people treat it like one (or approximately). Seems like the whole risk-neutral “probability” stuff. Also, this wouldn’t be the first time that people in finance (and tons of other fields) have been sloppy (or outright misused) statistics/probability.
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I just read both of those.
It’s sad what people will believe.
 
And while we’re on the subject of stupid option stuff, where did the idea arise that an ATM call option will have a delta of 0.5? That’s just plain silly.
 
S2000magician wrote:
And while we’re on the subject of stupid option stuff, where did the idea arise that an ATM call option will have a delta of 0.5? That’s just plain silly.
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I guess only when the time-premium of money is zero, or the time horizon is infinite
Or a binary option, or both. I don’t have MCS to test though.
 
S2000magician wrote:
And while we’re on the subject of stupid option stuff, where did the idea arise that an ATM call option will have a delta of 0.5? That’s just plain silly.
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I think some people assume that it’s equally likely to rise or fall over the next step in time. Similar to what they are saying in the link XK posted, if its the very last instant before expiration, and the option is ATM, it could make sense under the assumption of equiprobable up or down moves.
Other than that, it seems like a reallllly bad and loose approximation (based on your monte carlo simulations). I will say that I have heard people use it before as a probability, but I have more frequently heard it as a partial derivative of the option value with respect to the underlying’s price (you know, because that’s what it is…).
 
It is certainly true (in the B-S-M model) that as T approaches zero, the delta of an ATM call approaches 0.5.
It’s also true that if rf = 0 and σ = 0, the delta of an ATM call is 0.5. Not that anybody cares at that point.
In all other cases, the delta of an ATM call is greater than 0.5.
 
tickersu wrote:… I have more frequently heard it as a partial derivative of the option value with respect to the underlying’s price (you know, because that’s what it is…).
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Honestly, though, what percentage of people in finance are well-versed in multi-variate calculus?
Or versed at all?
We could consider that percentage to be the probability of a randomly selected person in financing being well-versed in multi-variate calculus. Furthermore, we could approximate that probability by using the delta of that person … .
Sorry … got carried away there.
 
S2000magician wrote:
I ran another set of simulations with σ = 30%:
  • Delta = 0.50, P(exercise) = 2.2%
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this thread is a car crash.. according to some random online calculator.. A stock price is $20.67 will give a $20.00 strike with 0.5 delta and the other inputs..
any non genius will tell you a stock price of $20.67 and strike of $20 you have a slightly > 50% chance of expiring in the money.
 
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