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Total Posts: 62
Joined: Jun 2007
Posted: 2018-02-02 16:35
Hello everyone,

problem: The gamma profile in strike space has jumps in it. The jumps occur at deterministic points.

model: To simplify, the model I'm using is made up of 6 segments in strike space. Each segment is a different function. It's almost the same concept as a cubic spline. There's an ATM point, 2 points on the call side (C1 and C2), and 2 points on the put side (P1 and P2):

P2 P1 F C1 C2

These points (P2, P1, C1, C2) are a function of:
a) Future Price
b) standard deviation = F * atmVol * sqrt(Time)
c) a scalar multiplier that the trader chooses to bring these points closer and further away from ATM.

for example:
C2 = F + c2 * F * atmVol * sqrt(Time)
P1 = F - p1 * F * atmVol * sqrt(Time)

c2 and p1 are the scalars that the traders can change.

Just like the concept of the cubic spline, I keep the Vol level and 1st derivative (wrt to strike) equal from the left and right sides at each of points (P2, P1, F, C1 and C2).

In addition, our atm Vol is a function of the future price:
atmVolLive = slope * (F_live - F_fixed) + atmVolFixed
(assume slope is +ve for this example)

Let's say, I want to compute Delta and Gamma for a strike that is just to the right of C1. My call of interest sits on the function that is between C1 and C2. I move the future price up and down F + dF and F - dF. When we compute the option price in the up step, the value of C1 increases for 2 reasons:
a) the future price went up
b) the atmVol went up
This puts our call of interest to the left of C1. Now our call rests on the function between ATM and C1.

This is causing the jump in my gamma profile. No coincidence, of course, these jumps occur at my 5 points mentioned above.

Question: Is there anything I can do to fix this? If so, what can I do?

Thank you,

P.S. The future options are vanilla (euro and american). I'm using Black-Scholes for the Euro and Barone-Adesi-Whaley for the American.
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