Strangle

A strangle is an options position consisting of a call option and a put option on the same underlying asset and with the same expiry, but with different strike prices. In the usual form the call's strike is above the current price and the put's strike is below it, so each leg is an out-of-the-money option. Buying both creates a long strangle, and selling both creates a short strangle.

Like the straddle, the strangle is a trade on how far the price will move, not on which way. Because out-of-the-money options are cheaper, a long strangle costs less than a straddle on the same asset, but the price must travel further before the position pays off. The short strangle is one of the most widely used positions for collecting option premium.

The profit at expiry is:

• $S_T$ is the price of the underlying at expiry.
• $K_c$ is the strike of the call and $K_p$ the strike of the put, with $K_p$ below $K_c$.
• $C$ and $P$ are the premiums paid for the call and the put.

The break-even prices are $K_c + (C + P)$ on the upside and $K_p - (C + P)$ on the downside. If the price finishes anywhere between the two strikes, both options expire worthless and the buyer loses the whole premium. That is the maximum loss. Beyond the break-even points the gain grows with the size of the move.

A share trades at $100. A trader buys a call with a strike price of $105 for $2.00 and a put with a strike of $95 for $1.80, both expiring in one month. The total cost is $3.80. The break-even prices are $105 + 3.80 = 108.80$ and $95 - 3.80 = 91.20$ dollars.

• At $115, the call is worth $10 and the profit is $10 - 3.80 = 6.20$ dollars per share.
• At $90, the put is worth $5 and the profit is $5 - 3.80 = 1.20$ dollars.
• At $107, the call is worth $2 and the result is $2 - 3.80 = -1.80$ dollars, a loss.
• At any price from $95 to $105, the loss is the full $3.80.

A straddle at the $100 strike might cost about twice as much, but it would begin to recover value as soon as the price left $100. The strangle is cheaper and has a wide zone of total loss.

The seller of a strangle receives the premium and keeps all of it if the price stays between the strikes until expiry. In the example the seller's maximum gain is $3.80, and the position is profitable anywhere between $91.20 and $108.80. Outside that range the loss grows without limit on the upside and down to a price of zero on the downside.

The appeal is a high probability of profit: the price usually does stay within a wide range over a short period. The seller is, in effect, collecting the volatility risk premium, the tendency of option prices to imply more movement than typically occurs. The cost is exposure to rare, large moves, which can erase the income of many months. Brokers require substantial margin for the position, and a sharp move can bring a margin call at the worst moment. Adding a further out-of-the-money call and put as protection converts a short strangle into an iron condor, which caps the loss.

A long strangle begins roughly neutral to small price changes and becomes directional as the price approaches one of the strikes. It has positive gamma and positive vega, so it benefits from large moves and from a rise in implied volatility. It has negative theta and loses value with each quiet day. The short strangle has the opposite signs.

The two legs are not always priced alike. In equity markets, out-of-the-money puts usually carry higher implied volatility than calls at the same distance, a feature called the volatility skew, so the put may cost more than the call.

Strikes are often selected by their delta instead of by a fixed distance from the price. A strangle built from options with deltas of about 0.16 places the strikes roughly one standard deviation away under the pricing model, and one with deltas of 0.30 places them closer. Wider strikes mean a lower premium and a lower chance that either option finishes in the money.

Shorter expiries bring faster time decay, which helps sellers and hurts buyers, but also greater sensitivity to sudden moves near expiry. Buyers typically use strangles ahead of events where a large move is possible and its direction is unclear, and face the same risk as with a straddle: implied volatility tends to fall once the event has passed, reducing the value of both options.