Derivative contracts can be used to construct strategies to profit from volatility. Straddle and choke option positions, volatility index options and futures can be used to profit from volatility.

## Cross-border strategy

In a straddle strategy, traders buy the same underlying call options and put options with the same strike price and the same period. This strategy enables traders to profit from changes in the underlying price, so traders expect increased volatility.

For example, suppose that a trader purchases a call option and a put option on a stock with a strike price of $40 and an expiration date of three months. Assume that the current stock price of the underlying is also $40. Therefore, these two options are traded in money. Assume that the annual risk-free interest rate is 2%, and the annual standard deviation of the underlying price change is 20%. According to the Black-Scholes model, we can estimate that the call option price is $1.69 and the put option price is $1.49. (The put option parity also predicts that the cost of the call option and the price of the put option are approximately $0.2.) The cost of this strategy includes the sum of the call option price and the put option price-$3.18. This strategy allows long positions to profit from any price change, regardless of whether the underlying price is rising or falling. Here is how the strategy can profit from volatility when prices are rising and falling:

Scenario 1: The price of the mark at expiry is higher than $40. In this case, the put option is worthless when it expires, and the trader exercises the call option to realize the value.

Scenario 2: The price of the mark at expiry is less than $40. In this case, the call option is worthless when it expires, and the trader exercises the put option to realize the value.

In order to profit from the strategy, traders need high enough volatility to cover the cost of the strategy, that is, the sum of the premium paid for the call options and the put options. Traders need to have volatility to reach a price above US$43.18 or below US$36.82. Suppose the price rises to $45. In this case, the put option is worthless when it expires, and the call option is rewarded: 45-40=5. Subtracting the cost of holding positions, we get a net profit of 1.82.

## Strangulation strategy

Due to the use of two at-the-money options, long straddle positions are costly. The cost of the position can be reduced by constructing an option position similar to a straddle option, but this time using an out-of-the-money option. This type of position is called “strangulation” and includes an out-of-the-money call option and an out-of-the-money put option. Since options are not valuable, the cost of this strategy will be lower than the straddle strategy described earlier.

Continuing the previous example, suppose the second trader purchases a call option with a strike price of $42 and a put option with a strike price of $38. Everything else is the same, the price of the call option is $0.82, and the price of the put option is $0.75. Therefore, the cost of this position is only $1.57, which is about 49% lower than the cost of a straddle position.

Although compared with straddle strategies, this strategy does not require a lot of investment, but it does require higher volatility to make money. You can see this by the length of the black arrow in the image below. In order to profit from this strategy, the volatility needs to be high enough for the price to be above US$43.57 or below US$36.43.

## Use Volatility Index (VIX) options and futures

Volatility index futures and options are direct tools for trading volatility. VIX is the implied volatility estimated based on the S&P500 option price. VIX options and futures allow traders to profit from changes in volatility regardless of the underlying price direction. These derivatives are traded on the Chicago Board Options Exchange (Cboe). If traders expect volatility to increase, they can buy VIX call options, and if they expect volatility to decrease, they may choose to buy VIX put options.

VIX’s futures strategy will be similar to that of any other underlying securities. If the expected volatility increases, the trader will enter a long futures position, and in the case of a decline in volatility expectations, the trader will enter a short futures position.

## Bottom line

Straddle positions involve at-the-money call options and put options, and strangling positions involve out-of-the-money call options and put options. These can be constructed to benefit from increased volatility. Volatility index options and futures traded on Cboe allow traders to directly bet on implied volatility, so that traders can benefit from changes in volatility regardless of direction.

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