What is the best function to build a Delta neutral Butterfly SPP?

Questions
1

Hello.

I would like to insert a delta neutral structured products in a model. The SP is a long butterfly spread and It can be constructed by purchasing one in-the-money call option at a lower strike price, while also selling two at-the-money call options and buying one out-of-the-money call option. I would like to find the strike price of the in-the-money call option to make the Delta of the SP = 0. I’m doing it using the function “findroot” because I used it in the past for a straddle and it worked but in this case not. Is there a better function to do it? Or am I using it in an incorrect way? The file with the code is attached.

Any help will be very precious for me.

Lorenzo

Butterfly code.nb (278 KB)

2

Solved

3

Hi Lorenzo,

Would you mind posting the solution?

4

Hello Rohit,
I’m sorry, I didn’t see your question before. I used the findroot function. I will post an example, probably tomorrow.

5

K[sigma_, k_, zeta_, Ka_, K_, Ko_, V_, S_] :=
x /. FindRoot[gs[sigma, k, zeta, Ka, x, Ko, V, S] == 0, {x, 100}][[1]]

Plot[{psi[sigmab, kb, zetab, Kab, 
   K[sigmab, kb, zetab, Kab, x, Kob, sqrtVb^2, Sb], Kob, sqrtVb^2, Sb,
    x, Tb], 
  phi[sigmab, kb, zetab, Kab, 
   K[sigmab, kb, zetab, Kab, x, Kob, sqrtVb^2, Sb], Kob, sqrtVb^2, Sb,
    x, Tb], 
  1 - (psi[sigmab, kb, zetab, Kab, 
      K[sigmab, kb, zetab, Kab, x, Kob, sqrtVb^2, Sb], Kob, sqrtVb^2, 
      Sb, x, Tb] + 
     phi[sigmab, kb, zetab, Kab, 
      K[sigmab, kb, zetab, Kab, x, Kob, sqrtVb^2, Sb], Kob, sqrtVb^2, 
      Sb, x, Tb])}, {x, 0, 10}]

This is an example. gs is the function to compute the delta of the structured product. Findroot finds the value of the strike price of a call option included in the structured product for which the structured product is delta neutral (gs=0).

6

Thanks!