Let's say you decide to buy a 2Y10Y ATM swaption straddle (i.e. buy 10 million ATM payer swaption and buy 10 million ATM receiver swaption). In order to delta hedge, I believe you would short the 2Y10Y forward swap.
My questions are:
How exactly does this delta hedging work? When do you profit from it (is it when there is a big move in realized volatility in the underlying forward swap)?
What needs to happen in order for you to get a positive payoff from this straddle?
I'm a bit confused on where exactly you're making the profits off of this trade.