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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:

  1. 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)?

  2. 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.

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Technically speaking the delta on a straddle is zero, so you wouldn't be delta hedging anything. However, if you are trading spot premium (and not doing forward premium - which is convention these days) - there will be some discounting curve delta associated that would need to be hedged. Reg 2/ (if you're not actively gamma hedging) what needs to happen is the 10y swap has to move beyond the breakeven yield (straddle premium/10y duration) for you to make money.

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