Delta and gamma for "knock-in bull spread"

[Johan Emil Rasmussen]

Hi all,

I am trying to price and hedge a "knock-in bull spread" via bloomberg.

The position is created by a long down-and in-call and a short down-and in call with a higher strike. The two options both have SP500 as underlying (which value at the start date, 08/08/2014 is 1930.1) and have the following stats:

Long down-and-in call:
Start date: 08/08/2014
Barrier: 95% (1833.5)
Strike: 120% (2316.12)
Type: European
Expiry: 3 years
Barrier end date: after 1 year (!)

Short down-and-in call:
Start date: 08/08/2014
Barrier: 95% (1833.5)
Strike: 130% (2509.13)
Type: European
Expiry: 3 years
Barrier end date: after 1 year (!)

As you can see, the barrier is only active during the first year of the option. If it hasn't been breached after 1 year, the option will be worthless.

My problem is, that bloomberg doesn't seem able to calculate the correct delta/gamma values.
See the attached images below

As you can see, all the dates chosen in this scenario are within the first year (where the barrier is still active) - the red line is in fact on the barrier expiration date.

First issue: Below the barrier (1833.5), the delta and gamma values should be the same as the delta and gamma values for a vanilla bull spread with the same characteristics, since the option has knocked in - this is not the case.

Second issue: When the delta is increasing (as just above the barrier level), the gamma should be positive. This is not the case, as we can see in the second image!

Can anyone help me? I don't know if Bloomberg has some issues, or if I am doing something wrong.
Thank you very much.

Best,
Johan

 

[financeguy]

This does look a little funky in a few different ways, but I have a guess on the gamma issue. This happens every so often with a numerical bumping method to calculate gamma within a model that hasn't been tweaked to specialize in a certain product. Let's say you're a bit above of the barrier and it hasn't yet triggered. The structure is short delta because you need this thing to knock in. The structure should also be long gamma: if the underlying goes up, your short delta will gradually tend to zero, and if the underlying goes down, you get shorter delta as you approach the barrier. You also generally want the underlying to be more volatile so that you have a greater chance of knocking in. Plus you're paying time decay on the structure, and if it doesn't knock in you lose your premium. This is all very characteristic of a long gamma position. But when the barrier gets hit, the delta jumps. You jump from short delta above the knock in point, to long delta on the other side of the knock in point as you now are long a vanilla call spread. So if you are using a rote numerical procedure to calculate gamma, it will see the delta getting much longer when it bumps the underlying down through the barrier, which will tell it to spit out a short gamma number.