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zmkramer
April 17th 2008, 12:40 PM
I don't think the solution to this question is correct. The question is about the delta of a gap option with a trigger price of 100 and a strike price of 130.

The problem with the solution is that it assumes that N(d2) is a function of S (which it really is when you think about it, well at least one of the variables that d1 and d2 are functions of). However if N(d1) and N(d2) are functions of S when we calculate delta for a normal call option we would get

partial derivative of C with respect to S

(assuming lamda = 0, r=0, K=1)

is equal to

[N'(d1) - N'(d2)]*(1/volatility*S*root(T))

N'(x) is the density function of a standard normal random variable at x

I think the gap delta should be equal to N(d1) using the trigger price as the strike price, I think that the only thing that would change in a gap option compared to an option where the trigger is equal to the strike would be the amount borrowed.

Anyone? Anyone?

Abraham Weishaus
April 17th 2008, 07:36 PM
In a standard option the extra terms cancel out. In a gap, they don't.