There are seven factors or variables that determine the price of an option. Of these seven variables, six have known values, and there is no ambiguity about their input values into an option pricing model. But the seventh variable—volatility—is only an estimate, and for this reason, it is the most important factor in determining the price of an option.

- The current price of the underlying –
*known* - Strike price –
*known* - Type of option (Call or Put) –
*known* - Time to the expiration of the option –
*known* - Risk-free interest rate –
*known* - Dividends on the underlying –
*known* - Volatility –
*unknown*

### Key Takeaways

- Options prices depend crucially on the estimated future volatility of the underlying asset.
- As a result, while all the other inputs to an option’s price are known, people will have varying expectations of volatility.
- Trading volatility, therefore, becomes a key set of strategies used by options traders.

## Historical vs. Implied Volatility

Volatility can either be historical or implied; both are expressed on an annualized basis in percentage terms. Historical volatility (HV) is the actual volatility demonstrated by the underlying over a period of time, such as the past month or year. Implied volatility (IV), on the other hand, is the level of volatility of the underlying that is implied by the current option price.

Implied volatility is far more relevant than historical volatility for options’ pricing because it looks forward. Think of implied volatility as peering through a somewhat murky windshield, while historical volatility is like looking into the rearview mirror. While the levels of historical and implied volatility for a specific stock or asset can be and often are very different, it makes intuitive sense that historical volatility can be an important determinant of implied volatility, just as the road traversed can give one an idea of what lies ahead.

All else being equal, an elevated level of implied volatility will result in a higher option price, while a depressed level of implied volatility will result in a lower option price. For example, volatility typically spikes around the time a company reports earnings. Thus, the implied volatility priced in by traders for this company’s options around “earnings season” will generally be significantly higher than volatility estimates during calmer times.

## Volatility, Vega, and More

The “Option Greek” that measures an option’s price sensitivity to implied volatility is known as Vega. Vega expresses the price change of an option for every 1% change in volatility of the underlying.

Two points should be noted with regard to volatility:

- Relative volatility is useful to avoid comparing apples to oranges in the options market. Relative volatility refers to the volatility of the stock at present compared to its volatility over a period of time. Suppose stock A’s at-the-money options expiring in one month have generally had an implied volatility of 10%, but are now showing an IV of 20%, while stock B’s one-month at-the-money options have historically had an IV of 30%, which has now risen to 35%. On a relative basis, although stock B has greater absolute volatility, it is apparent that A has had a bigger change in relative volatility.
- The overall level of volatility in the broad market is also an important consideration when evaluating an individual stock’s volatility. The best-known measure of market volatility is the Cboe Volatility Index (VIX), which measures the volatility of the S&P 500. Also known as the fear gauge, when the S&P 500 suffers a substantial decline, the VIX rises sharply; conversely, when the S&P 500 is ascending smoothly, the VIX will be becalmed.

The most fundamental principle of investing is buying low and selling high, and trading options is no different. So option traders will typically sell (or write) options when implied volatility is high because this is akin to selling or “going short” on volatility. Likewise, when implied volatility is low, options traders will buy options or “go long” on volatility.

Based on this discussion, here are five options strategies used by traders to trade volatility, ranked in order of increasing complexity. To illustrate the concepts, we’ll look at a historical example using Netflix Inc. (NFLX) options.

## Buy (or Go Long) Puts

When volatility is high, both in terms of the broad market and in relative terms for a specific stock, traders who are bearish on the stock may buy puts on it based on the twin premises of “buy high, sell higher,” and “the trend is your friend.”

For example, Netflix closed at $91.15 on Jan. 27, 2016, a 20% decline year-to-date, after more than doubling in 2015, when it was the best performing stock in the S&P 500. Say that traders who were bearish on the stock could buy a $90 put (i.e. strike price of $90) on the stock expiring in June 2016. The implied volatility of this put was 53% on Jan. 29, 2016, and it was offered at $11.40. This means that Netflix would have had to decline by $12.55 or 14% from those starting levels before the put position became profitable.

This strategy is a simple but relatively expensive one, so traders who want to reduce the cost of their long put position can either buy a further out-of-the-money put or can defray the cost of the long put position by adding a short put position at a lower price, a strategy known as a bear put spread.

Continuing with the Netflix example, a trader could have bought a June $80 put at $7.15, which was $4.25 or 37% cheaper than the $90 put at the time. Or else the trader could have looked to a bear put spread by buying the $90 put at $11.40 and selling (writing) the $80 put at $6.75 (note that the bid-ask for the June $80 put was thus $6.75 / $7.15), for a net cost of $4.65.

## Write (or Short) Calls

A trader who was also bearish on the stock but thought the level of implied volatility for the June options could recede might have considered writing naked calls on Netflix in order to pocket a premium of over $12. Assume that the June $90 calls had a bid-ask of $12.35/$12.80 on Jan. 29, 2016, so writing these calls would result in the trader receiving a premium of $12.35 (i.e. receiving the bid price).

If the stock closed at or below $90 by the June 17 expiration of those calls, the trader would have kept the full amount of the premium received. If the stock closed at $95 just before expiration, the $90 calls would have been worth $5, so the trader’s net gain would still be $7.35 (i.e. $12.35 – $5).

The Vega on the June $90 calls was 0.2216, so if the IV of 54% dropped sharply to 40% (i.e., 14 vols) soon after the short call position was initiated, the option price would have declined by about $3.10 (i.e. 14 x 0.2216).

Note that writing or shorting a naked call is a risky strategy, because of the theoretically unlimited risk if the underlying stock or asset surges in price. What if Netflix soared to $150 before the June expiration of the $90 naked call position? In that case, the $90 call would have been worth at least $60, and the trader would be looking at a large 385% loss. In order to mitigate this risk, traders will often combine the short call position with a long call position at a higher price in a strategy known as a bear call spread.

## Short Straddles or Strangles

In a straddle, the trader writes or sells a call and put at the same strike price in order to receive the premiums on both the short call and short put positions. The rationale for this strategy is that the trader expects IV to abate significantly by option expiry, allowing most if not all of the premium received on the short put and short call positions to be retained.

Again using the Netflix options as an example, writing the June $90 call and writing the June $90 put would have resulted in the trader receiving an option premium of $12.35 + $11.10 = $23.45. The trader was banking on the stock staying close to the $90 strike price by the time of option expiration in June.

Writing a short put imparts on the trader the obligation to buy the underlying at the strike price even if it plunges to zero while writing a short call has theoretically unlimited risk as noted earlier. However, the trader has some margin of safety based on the level of the premium received.

In this example, if the underlying Netflix stock closed above $66.55 (i.e. strike price of $90 – premium received of $23.45), or below $113.45 (i.e. $90 + $23.45) by option expiry in June, the strategy would have been profitable. The exact level of profitability depended on where the stock price was by option expiry; profitability was maximized at a stock price by expiration of $90 and reduced as the stock gets further away from the $90 level. If the stock closed below $66.55 or above $113.45 by option expiry, the strategy would have been unprofitable. Thus, $66.55 and $113.45 were the two break-even points for this short straddle strategy.

A short strangle is similar to a short straddle, the difference being that the strike price on the short put and short call positions are not the same. As a general rule, the call strike is above the put strike, and both are out-of-the-money and approximately equidistant from the current price of the underlying. Thus, with Netflix trading at $91.15, the trader could have written a June $80 put at $6.75 and a June $100 call at $8.20, to receive a net premium of $14.95 (i.e. $6.75 + $8.20). In return for receiving a lower level of premium, the risk of this strategy was mitigated to some extent. This is because the break-even points for the strategy became $65.05 ($80 – $14.95) and $114.95 ($100 + $14.95) respectively.

## Ratio Writing

Ratio writing simply means writing more options than are purchased. The simplest strategy uses a 2:1 ratio, with two options, sold or written for every option purchased. The rationale is to capitalize on a substantial fall in implied volatility before option expiration.

A trader using this strategy could have purchased a Netflix June $90 call at $12.80, and write (or short) two $100 calls at $8.20 each. The net premium received in this case was thus $3.60 (i.e. $8.20 x 2 – $12.80). This strategy is equivalent to a bull call spread (long June $90 call + short June $100 call) with a short call (June $100 call). The maximum gain from this strategy would accrue if the underlying stock closed exactly at $100 shortly before option expiration. In this case, the $90 long call would have been worth $10 while the two $100 short calls would expire worthlessly. The maximum gain would, therefore, be $10 + premium received of $3.60 = $13.60.

### Ratio Writing Benefits and Risks

Let’s consider some scenarios to evaluate the profitability or risk of this strategy. What if the stock closed at $95 by option expiry? In this case, the $90 long call would have been worth $5 and the two $100 short calls would expire worthless. The total gain would, therefore, have been $8.60 ($5 + net premium received of $3.60). If the stock closed at $90 or below by option expiry, all three calls expired worthless and the only gain would have been the net premium received of $3.60.

What if the stock closed above $100 by option expiry? In this case, the gain on the $90 long call would have been eroded by the loss on the two short $100 calls. At a stock price of $105, for example, the overall P/L would have been: $15 – (2 X $5) + $3.60 = $8.60

Break-even for this strategy would be at a stock price of $113.60 by option expiry, at which point the P/L would be: (profit on long $90 call + $3.60 net premium received) – (loss on two short $100 calls) = ($23.60 + $3.60) – (2 X 13.60) = 0. Thus, the strategy would be increasingly unprofitable if the stock rose above the break-even point of $113.60.

## Iron Condors

In an iron condor strategy, the trader combines a bear call spread with a bull put spread of the same expiration, hoping to capitalize on a retreat in volatility that will result in the stock trading in a narrow range during the life of the options.

The iron condor is constructed by selling an out-of-the-money (OTM) call and buying another call with a higher strike price while selling an in-the-money (ITM) put and buying another put with a lower strike price. Generally, the difference between the strike prices of the calls and puts is the same, and they are equidistant from the underlying. Using Netflix June option prices, an iron condor might involve selling the $95 call and buying the $100 call for a net credit (or premium received) of $1.45 (i.e. $10.15 – $8.70), and simultaneously selling the $85 put and buying the $80 put for a net credit of $1.65 (i.e. $8.80 – $7.15). The total credit received would, therefore, be $3.10.

The maximum gain from this strategy was equal to the net premium received ($3.10), which would accrue if the stock closed between $85 and $95 by option expiry. The maximum loss would occur if the stock at expiration was trading above the $100 call strike or below the $80 put strike. In this case, the maximum loss would be equal to the difference in the strike prices of the calls or puts respectively less the net premium received, or $1.90 (i.e. $5 – $3.10). The iron condor has a relatively low payoff, but the tradeoff is that the potential loss is also very limited.

## The Bottom Line

These five strategies are used by traders to capitalize on stocks or securities that exhibit high volatility. Since most of these strategies involve potentially unlimited losses or are quite complicated (like the iron condor strategy), they should only be used by expert options traders who are well versed with the risks of options trading. Beginners should stick to buying plain-vanilla calls or puts.