Delta of a bull spread at expiration

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philippmb

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Hi,
lets assume I have a bull spread with long Call (X=50) and short Call (X=56), and the share price is 53, what is the delta a day before expiration?
The solution is: close to 1, because the long Call has a delta of 1 (in the money) and the short calll a delta of 0 (OTM).
But I don´t understand why the bull spread overall has then a delta of 1. Wouldn´t it be around 0.5?
 
basically the deltas are additive.. not weighted (averaged)
think about how the entire position value changes.. in your example.. a dollar move higher (from 53 to 54) in the underlying would increase the value your options position by $1 regardless of what the worthless option is doing.. so delta =1
 
I think Phillipmb is assuming that since the stock is at 53 and the calls have strikes at 50&56 the overall position is ATM and expects a 0.5 delta.
 
delta only gets close to one at expiry. and only if the price is right in the middle of your strikes.
 
philippmb wrote:
Hi,
lets assume I have a bull spread with long Call (X=50) and short Call (X=56), and the share price is 53, what is the delta a day before expiration?
The solution is: close to 1, because the long Call has a delta of 1 (in the money) and the short calll a delta of 0 (OTM).
But I don´t understand why the bull spread overall has then a delta of 1. Wouldn´t it be around 0.5?
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Is one cause you are seeing the structure as a whole, as they say at 53 you are in the delta 1 interval. before expiration it is less than 1 because there is a probability of the share price to move beyond 56 or below 50, but at expiration is 1.
the “average” delta you’re reasoning does not apply, because as a partial derivative of the option to the underlying you do not average the deltas, in any case you add them, so 1+0 is 1.
 
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