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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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Agree with answer above - delta is roughly 0 ATMF. But it is model dependant.

As the 2y10y fwd moves, your straddle will accrue delta (new delta = old delta + gamma * curve move). so as you accrue delta, you may decide to delta hedge. Note if you are long the straddle, as the market sells off, you get shorter delta, as the market rallies you get longer.

  1. For eg. if the market sells off 20bps, you are now shorter say 20k Dv01 => you need to receive fixed (to flatten your risk). Now if the market rallies back 20bps you go to flat again => you need to pay the 20k you just received. You've net made money by just flattening your risk. This is gamma trading - for this grand privilege, you pay your daily carry. So if the market doesn't move at all, you just lose your theta. Therefore, gamma trading is all about weighing out implied vol (the cost of theta) versus realised vol (the actual volatility which the underlying endures during the life of the trade).

  2. The move to outweigh the premium spent: the 10y fixing needs to reach (strike) +/- premium spent/Dv01, at expiry of the trade for the straddle, for it to breakeven. i.e. it needs to end up more ITM on any side than what you paid for the options.

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