Delta Hedging and Gamma Trading a Swaption Straddle
Summary
The document explains how a near at-the-money payer and receiver swaption pair behaves as the underlying forward swap rate moves. Its initial delta is approximately zero, though the exact value depends on the pricing setup; spot-premium treatment can also introduce curve delta. As the rate moves, the long straddle gains delta through gamma, and a trader can trade the underlying swap to reduce that exposure and potentially earn from a move followed by a reversal.
The example describes receiving fixed after a selloff and later paying fixed if the rate rallies back, with a net gain from rebalancing. This gamma trading must be weighed against theta decay: quiet markets can leave the buyer losing carry, so profitability depends on realized movement relative to implied volatility priced into the options. At expiry, the rate must move far enough from the strike for intrinsic value to exceed the premium paid. The discussion is qualitative and omits transaction costs, hedge frequency, and detailed pricing assumptions.
Key ideas
- An at-the-money payer and receiver straddle has approximately zero initial delta, subject to model and premium conventions.
- As the forward swap rate moves, gamma changes the straddle’s delta and creates a need or opportunity to rebalance.
- A long straddle may earn through repeated delta hedging when realized movement compensates for option theta.
- At expiry, the underlying rate must move beyond the premium-adjusted breakeven for the straddle to profit.
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Full text
# Delta hedge swaption straddle # Delta hedge swaption straddle 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. ## Answer by user35980 (score 0) https://quant.stackexchange.com/a/70844 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. ## Answer by user68819 (score 0) https://quant.stackexchange.com/a/79558 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. - 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). - 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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