Strangle (options)

In finance, a strangle is an investment strategy involving the purchase or sale of particular option derivatives that allows the holder to profit based on how much the price of the underlying security moves, with relatively minimal exposure to the direction of price movement. The purchase of particular option derivatives is known as a long strangle, while the sale of the option derivatives is known as a short strangle. It is related to a similar option strategy known as a straddle.

Long strangle

The long strangle involves going long (buying) both a call option and a put option of the same underlying security. Like a straddle, the options expire at the same time, but unlike a straddle, the options have different strike prices. A strangle can be less expensive than a straddle if the strike prices are out-of-the-money. The owner of a long strangle makes a profit if the underlying price moves far enough away from the current price, either above or below. Thus, an investor may take a long strangle position if he thinks the underlying security is highly volatile, but does not know which direction it is going to move. This position is a limited risk, since the most a purchaser may lose is the cost of both options. At the same time, there is unlimited profit potential.[1]

Short strangle

payoff of short strangle

The short strangle involves shorting (selling) both a call option and a put option of the same underlying security. Like a short straddle, the options expire at the same time, but unlike a straddle, the options have different strike prices. The premium can be chosen by the short party, with the hope that this will cover any potential volatility. The short party of the strangle makes a profit if the underlying price stays within the boundaries of the strike price of which they would be exercised, either above or below. Thus, an investor may take a short strangle position if he thinks the underlying security is not at all volatile. This position has limited profit and unlimited risk. A long iron condor is similar, but due to the wings it has limited downside.

$S_{25} = \sigma_{put,25} - 2 \sigma_{atmf} + \sigma_{call,25}$
where $\sigma_{put,25}$ is the volatility of the put with the strike chosen to give a delta of -25%.
$\sigma_{call,25}$ is the volatility of the call with the strike chosen to give a delta of 25%.
and $\sigma_{atmf}$ is the volatility of call with strike set to the forward.