Let's have a look at how we talk about Vega and Theta. Here FX options look much more similar to other options in that vega and theta are just reported as cash numbers.
To turn our raw Black-Scholes risk metric into a cash figure, we multiply it by the notional of the trade in the base currency, and we get the cash amount of risk in the quoted currency. In this example, we have a 1.10 in Euro dollar with a Black-Scholes vega of 0.003 and a theta of minus 0.00006. If we buy 10 million Euro notional of this option, then we are long $30,100 of vega, and we are paying $622 of theta per day. Generally, the natural increment on vega is per 1% move in vol in absolute terms. For example, a move from 8% to 9%. Sometimes we may reduce this increment to see our risk to a more realistic move in vol, or we may recognize that not all vols move by the same fixed increment, so we may calculate a vega by modeling what happens when all vols change by a certain percentage of this starting values.
For example, a 10% scaling would mean a 10% vol moves to 11%, and a 15% vol moves to 16.5%. Some traders think this gives a vago, which is a more realistic estimate of how vols will really move. For theta, the standard increment is per day. However, for very short dated options, for example, an overnight or one day option, it may be more appropriate to model theta over a smaller time increment, like one hour rather than one day.
