Seven factors determine the price of an option. Six have known values, and there is no ambiguity about their input values in an option pricing model. The seventh variable, volatility, is only an estimate and 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
- Options prices depend on the estimated future volatility of the underlying asset.
- While other inputs to an option's price are known, investors expect varying levels of volatility.
- Trading volatility requires a set of strategies used by options traders.
Historical vs. Implied Volatility
Volatility can be historical or implied, expressed on an annualized basis in percentage terms. Historical volatility (HV) is the actual volatility demonstrated by the underlying asset over some time, such as the past month or year. Implied volatility (IV) is the level of volatility of the underlying implied by the current option price.
Implied volatility is more relevant than historical volatility for options’ pricing because it looks forward. While historical and implied volatility for a specific stock or asset differs, historical volatility can be a determinant of implied volatility.
An elevated level of implied volatility will result in a higher option price, and a depressed level of implied volatility will result in a lower option price. 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 and Vega
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 asset.
- Relative volatility refers to the volatility of the stock at present compared to its volatility over some 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.
Option traders 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.
1. Go Long Puts
When volatility is high, traders who are bearish on the stock may buy puts based on the twin premises of “buy high, sell higher,” and “the trend is your friend.”
For example, Company A closed at $91.15 on Jan. 27th. Traders bearish on the stock could buy a $90 put, or strike price of $90 on the stock expiring in June. The implied volatility of this put was 53% on Jan. 29th, and it was offered at $11.40. Company A would have had to decline by $12.55 or 14% from those starting levels before the put position is profitable.
Traders who want to reduce the cost of their long put position can either buy a further out-of-the-money (OTM) put or 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. 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 chosen a bear put spread by buying the $90 put at $11.40 and selling (writing) the $80 put at $6.75. The bid-ask for the June $80 put was thus $6.75 / $7.15), for a net cost of $4.65.
2. Short Calls
A trader who is bearish on the stock but hoping the level of implied volatility for the June options could recede might have considered writing naked calls on Company A for a premium of over $12. Assume that the June $90 calls had a bid-ask of $12.35/$12.80 on Jan. 29th, so writing these calls would result in the trader receiving a premium of $12.35 or 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 ($12.35 - $5). Assume the Vega on the June $90 calls was 0.2216. If the IV of 54% dropped sharply to 40% (14 vols) soon after the short call position was initiated, the option price would have declined by about $3.10 (14 x 0.2216).
Writing or shorting a naked call is a risky strategy, because of the unlimited risk if the underlying stock or asset surges in price. What if Company A 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. To mitigate this risk, traders often combine the short call position with a long call position at a higher price in a strategy known as a bear call spread.
3. Short Straddles or Strangles
In a straddle, the trader writes or sells a call and put at the same strike price to receive the premiums on both the short call and short put positions. The trader expects IV to abate significantly by option expiry, allowing most of the premium received on the short put and short call positions to be retained.
For Company A, 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 anticipated the stock staying close to the $90 strike price by the time of option expiration in June.
Writing a short put requires the trader to buy the underlying at the strike price even if it plunges to zero while writing a short call has unlimited risk. However, the trader has some margin of safety based on the level of the premium received.
If the underlying Company A stock closed above $66.55 (strike price of $90 - premium received of $23.45) or below $113.45 ($90 + $23.45) by option expiry in June, the strategy would have been profitable. The exact level of profitability depends 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, but the strike price on the short put and short call positions are not the same. 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. With Company A 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 ($6.75 + $8.20). In return for receiving a lower level of premium, the risk of this strategy was mitigated because the break-even points for the strategy became $65.05 ($80 - $14.95) and $114.95 ($100 + $14.95).
4. Ratio Writing
Ratio writing 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 Company A 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 $3.60 ($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 accrues 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 be $10 + premium received of $3.60 = $13.60.
Ratio Writing Benefits and Risks
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 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. The strategy is increasingly unprofitable if the stock rises above the break-even point of $113.60.
5. Iron Condors
In an iron condor strategy, the trader combines a bear call spread with a bull put spread of the same expiration 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 writing a put OTM below the current stock price or spot price.
Generally, the difference between the strike prices of the calls and puts is the same, and they are equidistant from the underlying. Using Company A's June option prices, an iron condor might involve selling the $95 call and buying the $100 call for a premium received of $1.45 ($10.15 - $8.70) and simultaneously selling the $85 put and buying the $80 put for a net credit of $1.65 ($8.80 - $7.15). The total credit received is $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 occurs if the stock at expiration trades above the $100 call strike or below the $80 put strike. The maximum loss would equal the difference in the strike prices of the calls or puts, respectively, less the net premium received, or $1.90 ($5 - $3.10). The iron condor has a relatively low payoff, and loss is limited.
What 7 Factors Determine the Price of an Option?
The current price of the underlying asset, the strike price, the type of option, time of expiration, the interest rate, dividends of the underlying option, and volatility.
What Is the Difference Between Historical and Implied Volatility?
Historical volatility is the actual volatility demonstrated by the underlying asset over time. Implied volatility is the level of volatility of the underlying implied by the current option price.
What Is the Main Goal of the Iron Condor Stategy?
The iron condor earns the maximum profit when the underlying asset closes between the middle strike prices at expiration. The goal is to profit from low volatility in the underlying asset.
The Bottom Line
Five strategies are used by traders to capitalize on stocks or securities that exhibit high volatility. Most of these strategies involve unlimited losses and can be complicated. They should only be used by expert options traders who are well-versed in the risks of options trading.
Correction–May 10, 2023: This article has been amended to clarify that the iron condor is constructed by writing a put OTM, which is below the current spot price.