# What is the formula for beta weighted delta and gamma?

I am trying to calculate the beta weighted delta and gamma for a portfolio of options of different underlying stocks, but I can't seem to find the correct formula.

Can someone point me to it or a book that contains it?

• What is beta weighted? Is it under Black Scholes model? – emcor Oct 22 '14 at 20:21
• By beta weighting I mean, using the beta of the underlying stock to use with the individual options that make up a portoflio to come up with a delta of entire portfolio. – CptanPanic Oct 23 '14 at 11:35

In short: $$\beta_{\text{option}} = \frac{S\cdot\Delta}{O}{\beta_S}$$ where $S$ is the underlying price ($x$ in the B&S paper), $O$ is the option price ($w_1$ in B&S), $\Delta$ is the usual $\partial{O}/\partial{S}$, and $\beta_S$ is $\beta$ for the underlying.
Regarding your question, you'd just have to re-arrange this to use an empirically measured option $\beta$, and differentiate for Gamma. I'm not sure that gets you where you want to go, though.