# Greeks of portfolio in response to underlying price change

I'm trying to wrap my head around Greeks, and I'm getting a little bit confused. For example, let's say my portfolio holds a long 5 month ATM call with strike \$20, and short 2 month OTM call with strike \$60. Now, if my underlying rises to \$40, what happens to my $$\Delta$$, $$\Gamma$$ and $$\nu$$ega exposures? I'm not exactly sure how much information I can say looking at the Black-Scholes formula since I don't have information about $$\sigma$$, so what can I say about the response of the Greeks to this underlying change? • You don't mention what your starting value is (also of Greeks like delta, seems you are very far away from ATM so potentially neither delta nor gamma changes much). Without knowing sigma, you cannot talk about Greeks really. Oct 14 at 12:43 • @AKdemy thanks for the comment, which starting value do you mean? Is it still not possible to get an intuition for how the Greeks (exposures, I rephrased it a little bit) change without plugging into the B-S equation? Oct 14 at 12:50 • The$\Gamma$gives you insight into how$\Delta$changes if$S\$ changes. This is true on a portfolio level and not just for a single option. What is the sign of your overall Gamma? Oct 14 at 13:15
• What is your current underlying price? Could be any real number. without an option pricing model (or any idea what your values are), how would you want to compute something that purely depends on a model? What is the purposes of the question even? If you are asking how Greeks of two options (portfolio) work, that's simply the sum of the individual options. Oct 14 at 13:16
• Ok, missed the ATM part. Delta will be somewhere close to 0.5 for ATM. The other is so far otm it will likely be zero.if your underlying doubles, Greeks will be useless as anything that jumps like this will not qualify for infinitesimally small changes (what Greeks show). In any case, you need a model to talk about Greeks. What is the context/ background of this question? Oct 14 at 13:38

$$P \approx P_0 + \Delta * dS + \frac12 * \Gamma * (dS)^2$$
But you asked about the effects on $$\Delta$$, $$\Gamma$$, and vega. Gamma will give you an approximate change in delta ($$d\Delta \approx \Gamma*dS$$). There are greeks that will tell you the change in Gamma and Vega when the underlying changes (Speed and Vanna, respectively), but they are not as widely used.