Portfolio Greek Exposure Equations

Question

What are the calculations for calculating greek exposures in a portfolio of equities and equity options? I think I have them but I want to be sure. Are these correct (for vanilla options)?

deltaDollars = delta * quantity * 100

gammaDollars = gamma * quantity * 100

vegaDollars = vega * quantity * 100

thetaDollars = theta * quantity * 100

rhoDollars = rho * quantity * 100

I think that for calculating exposures for a whole portfolio, I can sum up these values for each position in the whole portfolio. Is this correct?

I am not sure about summing gammaDollars in this way because gamma is a second derivative. If my portfolio has only these positions:

• 23 MSFT options (gamma = 0.1, gammaDollars = $230)

• 29 AAPL options (gamma = 0.2, gammaDollars = $580)

Can I say that my portfolio's gammaDollars are \$810 (\$230 + \$580)? Or can I not add the numbers in this way?

Answer 1

I, personally, like to see gamma as change in dollar delta per percent (most systems have it as "GammaP"). This way, it's much easier to think about you delta position as the market is moving around.

The number above is the BS gamma which is an unscaled 2nd derivative of delta. You need to rescale it to get gammap (delta change per percent). In general, it is also a good idea to calculate your delta and especially gamma using sticky strike volatilities - the easiest way to do so is to look at implied vol on the adjusted strikes and reprice your option using that vol and spot bumped up/down by the strike spread.