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

In this 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 annual risk free rate is 2% and 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 long position to profit from any price change no matter if the price of the underlying 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 exercise 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.

Even though this strategy does not require large investment compared to the straddle, it does require higher volatility to make money. You can see this with the length of the black arrow in the graph below. In order to make a profit from this strategy, volatility needs to be high enough to make the price either above \$43.57 or below \$36.43.

## Using Volatility Index (VIX) Options and Futures

Volatility index futures and options are direct tools to trade volatility. VIX is the implied volatility estimated based on S&P500 option prices. VIX options and futures allow traders to profit from the change in volatility regardless of the underlying price direction. These derivatives are traded on the Chicago Board Options Exchange (CBOE). If the trader expects an increase in volatility, she can buy a VIX call option, and if she expects a decrease in volatility, she may choose to buy a VIX put option.

Futures strategies on VIX will be similar to those on any other underlying. The trader will enter into a long futures position if she expects increase in volatility and into a short futures position in case of an expected decrease in volatility.

## The Bottom Line

The straddle position involves at-the-money call and put options, and the strangle position involves out-of-the-money call and put options. These can be constructed to benefit from increasing volatility. Volatility Index options and futures traded on the CBOE allow the traders to bet directly on the implied volatility, enabling traders to benefit from the change in volatility no matter the direction.

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