Straddle

A straddle is an options position that consists of a call option and a put option on the same underlying asset, with the same strike price and the same expiry date. A trader who buys both options holds a long straddle, which profits if the underlying price moves far enough from the strike in either direction. A trader who sells both holds a short straddle, which profits if the price stays close to the strike.

The straddle is the simplest way to trade the size of a price move without taking a view on its direction. The strike is usually chosen at or near the current price, making both legs an at-the-money option. Unless stated otherwise, the term refers to the long position, which is the subject of most of this entry.

The profit of a long straddle at expiry is:

• $S_T$ is the price of the underlying asset at expiry.
• $K$ is the strike price shared by both options.
• $C$ and $P$ are the premiums paid for the call and the put.

The position breaks even when the underlying has moved away from the strike by exactly the total premium, so the two break-even prices are $K + (C + P)$ and $K - (C + P)$. The maximum loss is the total premium, incurred if the price finishes exactly at the strike and both options expire worthless. The potential gain is unlimited on the upside and very large on the downside, limited only by the price falling to zero.

A share trades at $100. A trader buys a one-month call with a strike of $100 for $4.00 and a one-month put with the same strike for $3.50, paying $7.50 in total. The break-even prices are $107.50 and $92.50.

• If the share is at $115 at expiry, the call is worth $15 and the put nothing. The profit is $15 - 7.50 = 7.50$ dollars per share.
• If the share is at $88, the put is worth $12 and the call nothing. The profit is $12 - 7.50 = 4.50$ dollars.
• If the share is at $103, the call is worth $3. The result is $3 - 7.50 = -4.50$ dollars, a loss.
• If the share is at $100, both options expire worthless and the full $7.50 is lost.

Options on shares usually cover 100 shares each, so these figures are multiplied by 100 per straddle.

The price of an at-the-money straddle shows how large a move the market is pricing in before expiry. In the example, the $7.50 premium implies an expected move of roughly 7.5 percent. Traders routinely read the straddle price ahead of earnings announcements and other scheduled events for this purpose.

A useful approximation links the price to implied volatility:

Here $S$ is the current price, $\sigma$ the annual implied volatility and $T$ the time to expiry in years. With a price of $100, volatility of 30 percent and 30 days to expiry, $\sqrt{30 / 365} = 0.287$ and the estimate is $0.8 \times 100 \times 0.30 \times 0.287 = 6.88$ dollars.

At the outset a long straddle is close to delta neutral, since the positive delta of the call offsets the negative delta of the put. It has positive gamma, so it gains exposure in the direction of any move. It has positive vega, gaining value if implied volatility rises, and negative theta, losing value each day that the price does not move.

These features make the straddle a direct trade on volatility. The buyer profits when the realized volatility of the underlying exceeds the implied volatility paid. Professional traders often hedge the delta repeatedly as the price moves, a practice called gamma scalping, to collect that difference without waiting for expiry.

The main risk for a buyer is that the move is smaller than the premium implies. Options are often most expensive just before a known event, and implied volatility typically drops sharply once the event has passed. A straddle bought before an earnings release can therefore lose money even when the share moves, if the move is less than the market had priced. Time decay is fastest in the final weeks before expiry, and two sets of bid-ask spreads and commissions are paid.

For a seller, the risks are reversed and more severe. The short straddle earns a limited premium and faces losses that are theoretically unlimited, so it requires margin and close monitoring. On average, implied volatility on equity indices has exceeded subsequent realized volatility, which has favoured sellers over long periods, but those gains have been interrupted by large losses in market shocks.

A related position, the strangle, uses a call and a put with different strikes. It costs less than a straddle but needs a larger move to become profitable.