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# Delta-Gamma Neutral Self Financing

Discussion in 'Options' started by eagertolearn, May 12, 2007.

1. ### eagertolearn

I'm trying to design a position for an investor who would like to benefit from an increase in volatility by
5% percentage points in the amount of \$1000 but would like to be delta and gamma neutral, and have
the portfolio designed be self financing.

The spot price on the underlying asset is \$100 with a continuously compounded interest rate
of 6% and a dividend yield of 2%, also continuously compounded. A three month put struck at 80 and
a six month call struck at 120 have the following information:

80Put maturity=0.25 120Call maturity=.5
Price 2.0836 7.9372
Delta -0.1444 0.3849
Gamma 0.008929 0.01376
Vega 11.3458 16.9264

Any ideas on how to start/go about this. I know it is relatively simple, but I am still learning

2. ### demoship

You also want to be theta neutral if you're holding long options for a while.

3. ### cvds16

The answer is just a simple set of equations and solving them

what is the rate of speed in vols increase ? IOW , when your investor expecting volatility to become X+5 ?

5. ### cvds16

There is a lot of information too much here
I would need to do the detailed job myself, but from what I think (i'm better at the real thing than these artificial made up examples)
you would need to solve three equations
with x number of puts, y number of calls and z number of stock
x*-0.1444 + y*0.3849 + z = 0 for deltaneutrality
x*0.008929+ y* 0.01376 = 0 for gammaneutrality
(x*11.3458+y*16.9264)*5 = 1000 for the increase in vol
the rest is basic math

6. ### cvds16

I did this a bit too fast and forgot to multiply the delta's and gamma's en the vega by 100, so the equations need some (minor) adjustments

7. ### eagertolearn

Thanks so much....just curious though how the maturity, strikes, and dividend yield play into designing the position.

8. ### cvds16

they all influence the delta, gamma and vega figures through the option model used.

9. ### atticus

A long time fly or a long ratio calendar would be the position of choice in limiting your greek mag and drift. Regardless, it would require fairly discrete hedging.

10. ### Profitaker

The only position I can think of that's both delta neutral and gamma neutral is a box spread. But unfortunately it's also vega neutral so you wouldn't benefit from rising IV.

Perhaps the easiest way would be to do something with VIX futures or options ?

#10     May 13, 2007
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