I have a MC simulation that uses finite differences to calculate the Greeks. It's for baskets and calendar spreads mostly.
Now the logical (to me anyway) approach to calculate Vega is to increase the input volatility by 1% (annual vol) for each leg (leg1 Vega: leg1 vol + 1%, leg2 Vega: leg2 vol + 1%, etc.), reprice, then subtract the initial price, leg by leg. Result = $ change from a 1% volatility increase on each leg of the option.
Today, my boss told me I should be using a much smaller number than 1% (as a FD shock). I responded: but isn't Vega supposed to show you the change in option value with a 1% increase in volatility (annualized)? Did I miss something here? Please if there are other methods, or I am completely wrong in my approach, I really need to know. And if my method is satisfactory, please confirm as well.
Note on my background: I came from a market risk role, and transfered into derivatives pricing. Not the other way around, so my understanding of the meaning of Vega is the way it is understood in market risk. It may very well be looked at differently from a financial engineering perspective, but that is news to me.
Thanks for your time.