Straddle and strangle

A straddle is a call and a put with the same strike and expiry, usually at the money. A strangle uses an out-of-the-money put and an out-of-the-money call, so it is cheaper but needs a larger move. Both are volatility positions: the buyer wants movement, the seller wants calm.

How it works

At inception a straddle is close to delta neutral and carries the maximum gamma and vega for its expiry. A useful approximation for an at-the-money straddle is: price ≈ 0.8 × spot × implied volatility × √(time in years). At expiry, the buyer profits if the underlying ends beyond the strike plus or minus the premium. Before expiry, the P&L depends on realised volatility against implied, and on changes in implied volatility itself. The strangle has the same logic with lower gamma at inception and a wider zone where it loses everything.

Example

Hypothetical: a stock trades at 100 and one-month implied volatility is 20%. The approximation gives 0.8 × 100 × 20% × √(1/12), about 4.62. Say the call and the put each cost 2.30, so the straddle costs 4.60. Breakevens at expiry are 95.40 and 104.60. A strangle made of the 95 put at 0.75 and the 105 call at 0.50 costs 1.25, with breakevens at 93.75 and 106.25.

On the desk

Holders of a straddle usually delta hedge it, so the result depends on the path, not just the final price. Short strangles look comfortable because the strikes are far away, yet the losses in a gap move are open-ended.