0
$\begingroup$

We have an option portfolio with delta =2 and gamma 3 and we want to making this portfolio delta and gamma neutral using two derivatives D1 and D2:

------------------------
|        |Delta | Gamma|
------------------------
| Option | 2    | 3    |
------------------------
| D1     | -1   | 2    |
------------------------
| D2     | 5    | -2   |
------------------------

I have tried two ways for solving this and they both give different answers:

1)

$w_{D1}*\Delta_{D1} + w_{D2}*\Delta_{D2} = -2$ $w_{D1}*\Gamma_{D1} + w_{D2}*\Gamma_{D2} = -3$

With answers: $w_{D1}$ = -4/9 and $w_{D2}$ = -1/9

2)

$2 -1w_{D1} + 5w_{D2} = 0$;

$3 + 2w_{D1} + -2w_{D2} = 0$

With answers: $w_{D1}$ = -19/8 and $w_{D2}$ = -7/8

Can someone tell me where I do go wrong and give an interpretation of the results? Which technique should be used?

$\endgroup$
0
$\begingroup$

The two formulations seem to be exactly the same. If I take the equations from the first method:

$w_{D1}*\Delta_{D1} + w_{D2}*\Delta_{D2} = -2$

$w_{D1}*\Gamma_{D1} + w_{D2}*\Gamma_{D2} = -3$

And substitute for delta and gamma of the two options:

$-w_{D1}+ 5 w_{D2}= -2$

$2w_{D1} -2w_{D2} = -3$

which after shifting the constants to the left becomes exactly the same set as in method 2:

$2-w_{D1}+ 5 w_{D2}= 0$

$3+2w_{D1} -2w_{D2} = 0$

Maybe there is a typo in the solution method you used when solving the first set of equations.

$\endgroup$
  • $\begingroup$ Can you calculate the hedge and see the outcome? $\endgroup$ – sc_ams Jan 12 at 14:42
  • $\begingroup$ the second solution looks correct - you can verify by just plugging in the computed weights into the two equations, i.e,: −19÷8×−1−7÷8×5=-2, and −19÷8×2−7÷8×−2=-3 $\endgroup$ – Magic is in the chain Jan 12 at 14:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.