If I write the value of an option as O(S, K, T, V), where S is the underlying price, K is the strike, T is the time to expiry and V the implied volatility, how can I compute the dollar amount that I am expected to gain or lose based on specific movements in some of the variables? I know this is what the greeks should tell me and if I use Black and Scholes formula, there are equations for each of the greeks of interest. But I am not sure how to use them to express the move in dollar amount. Let's say that the underlying S moves 1% and that implied volatility moves 1% (in terms of volatility points, i.e. not relative move).
If I want the $ P&L associated to the delta, I can calculate the delta as:
Delta = O(S*1.01, K, T, V) - O(S, K, T, V)
i.e. the difference in option value if the underlying moves up by 1%. For Vega I can do:
Vega = O(S, K, T, V+1%) - O(S, K, T, V)
But what if I want to measure the P&L given by gamma, vanna and volga?