Can't figure out a basic question
- Thread starter LucasX
- Start date
Yes, I realized I read the question wrong. Sorry. I did not realize he was forcing the skew to be zero. He threw me off by saying the "same IV" instead of just saying the same vol. IV by definition is backed out from prices. You cannot assign it anything you want.
In that case, spindr0 your previous answer seems correct.
Look at it this way. If silver is at $5 an ounce, which would you rather own, the $1 puts or the $9 calls? Obviously the $9 calls.
If silver were just as likely to go down to -$5/oz as to go up to +$15/oz, then the two options should be priced the same. But if you assume that silver won't go below zero, then obviously the $9 calls are worth more.
Another way of looking at the lognormal distribution is that every time silver goes up, say, $1, it takes a smaller percentage move to do it. From 8 to 9 requires just a 12.5% move. But from 2 to 1 requires a 50% move. So as silver goes up, it becomes statistically "easier" - keeps requiring a smaller and smaller percentage move to go a fixed amount. As silver goes down, it becomes progressively "harder" in that it requires a greater and greater percentage move to go the same fixed amount.
If silver were just as likely to go down to -$5/oz as to go up to +$15/oz, then the two options should be priced the same. But if you assume that silver won't go below zero, then obviously the $9 calls are worth more.
Another way of looking at the lognormal distribution is that every time silver goes up, say, $1, it takes a smaller percentage move to do it. From 8 to 9 requires just a 12.5% move. But from 2 to 1 requires a 50% move. So as silver goes up, it becomes statistically "easier" - keeps requiring a smaller and smaller percentage move to go a fixed amount. As silver goes down, it becomes progressively "harder" in that it requires a greater and greater percentage move to go the same fixed amount.
How about another, sorta similar, question (same setting)?
Delta > 100%, in absolute value. Is that possible? If yes, under which conditions? If not, why?
Delta > 100%, in absolute value. Is that possible? If yes, under which conditions? If not, why?
Uh oh Mark, now you've done it. You've made Master at Work mad.
There've been lots of discussions in the past in which MAW has insisted that delta can be > 1 if interest rates are negative. I'll bet that's what Martin is referring to.
Honestly I can't remember the details but after first dismissing the idea out of hand, I recall having to grudgingly admit that MAW may have a point after all. I don't think that has a big effect on my day-to-day life, but perhaps in FX option trading - where I presume they deal with negative interest rates on a regular basis (interest rate of currency A minus interest rate of currency B) - it may be a consideration.
I was referring to a case for a deep ITM call, where cost-of-carry is greater than the risk-free rate. In that case, from what I can tell, this deep ITM call will have a spot delta that's greater than one, simply because of the PV effect. That's the explanation that's always made the most sense to me, anyways...