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# Dual Gamma and Dual Theta

Discussion in 'Options' started by bines, Sep 7, 2008.

1. ### bines

It's possible to receive a short explanation what the intention

thanks

2. ### dd4nyc

Dual gamma to gamma is same as dual delta to delta

Formally it is the second derivative w.r.t strike; how fast dual delta changes with strike.

You can use dual gamma and dual delta to calculate market implied deltas and gammas in an (almost) model-free manner. Other than that I don't see any use.

Dual theta is different from other "dual greeks" - it is the change in theta with respect to time, or theta decay.

As you move closer to expiration for ATM option theta grows, as your option decays faster and faster. However the rate of theta change is slowing down. There's not much interesting stuff here.

However if you look at OTM options these patterns become a lot more interesting. If you plot of theta you will see that theta does not simply grows until expiration, instead it has a peak after which theta declines. This makes dual theta look like a letter " L " as theta is growing at first and then declining. Practically this means that if you're trying to sell premium, there is an optimal point in time to do that - where theta peaks and dual theta becomes positive. This time is of course is different for every option.

If you have a software package that allows you to calibrate skew models ( for example Heston model) you can track dual theta to figure out the shape of theta. However if you rely on a retail package that uses black-scholes the numbers that you get for dual theta (or most of the greeks) are possibly (probably) not very accurate.

For higher order greeks you may wish to consult

http://en.wikipedia.org/wiki/Greeks_(finance)

particularly notes by Uwe Wystup.

3. ### bines

Hello ,dd4nyc

I understand that Dual gamma is positive.
= Exp(-Rate * Time) * n'(d2) / (Strike * Volatility * Sqrt(Time))
If there is a formula for dual theta ?

4. ### dd4nyc

I don't know of a formula, but why do you want it?

5. ### bines

Hello ,dd4nyc
I didn't understand, how you are a computer where theta peaks and dual theta becomes positive ?

6. ### dd4nyc

Calculate theta for different time to expiration holding all other parameters constant. The function will have a point of maximum.

7. ### bines

thank you !

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