Derivative contracts can be used to build strategies to profit from volatility. Straddle and strangle options positions, volatility index options, and futures can be used to make a profit from volatility.

In a straddle strategy, a trader purchases a call option and a put option on the same underlying with the same strike price and with the same maturity. The strategy enables the trader to profit from the underlying price change direction, thus the trader expects volatility to increase.

For example, suppose a trader buys a call and a put option on a stock with a strike price of \$40 and time to maturity of three months. Suppose that the current stock price of the underlying is also \$40. Thus both options are trading at the money. Imagine that the annual risk-free rate is 2% and the annual standard deviation of the underlying price change is 20%. Based on the Black-Scholes model we can estimate that the call price is \$1.69 and the put price is \$1.49. (Put-call parity also predicts that the cost of the call and put price are approximately \$0.2.) The cost of the strategy comprises the sum of the call and put prices—\$3.18. The strategy allows a long position to profit from any price change no matter if the price of the underlying is increasing or decreasing. Here is how the strategy makes money from volatility under both price increase and decrease scenarios:

Scenario 1: The underlying price at maturity is higher than \$40. In this case, the put option expires worthless and the trader exercises the call option to realize the value.

Scenario 2: The underlying price at maturity is lower than \$40. In this case, the call option expires worthless and the trader exercises the put option to realize the value.

In order to profit from the strategy, the trader needs volatility to be high enough to cover the cost of the strategy, which is the sum of the premiums paid for the call and put options. The trader needs to have volatility to achieve the price either more than \$43.18 or less than \$36.82. Suppose that the price increases to \$45. In this case, the put option expires worthless and the call pays off: 45-40=5. Subtracting the cost of the position, we get a net profit of 1.82.

## Strangle Strategy

A long straddle position is costly due to the use of two at-the-money options. The cost of the position can be decreased by constructing option positions similar to a straddle but this time using out-of-the-money options. This position is called a "strangle" and includes an out-of-the-money call and an out-of-the-money put. Since the options are out of the money, this strategy will cost less than the straddle illustrated previously.

To continue with the previous example, imagine that a second trader buys a call option with a strike price of \$42 and a put option with a strike price of \$38. Everything else the same, the price of the call option will be \$0.82 and the price of the put option will be \$0.75. Thus, the cost of the position is only \$1.57, approximately 49% less than that of the straddle position.