Technical Information

Volatility literally represents the standard deviation of day-to-day price changes in a security, expressed as an annualized percentage. Two measures of volatility are commonly used in options trading: historical and implied. Historical volatility depicts the degree of price change in an underlying security observed over a specified period of time using standard statistical measures. It is not a forecast of future volatility. Implied volatility is the market's prediction of expected volatility, which is indirectly calculated from current options prices using an option-pricing model. The exact formula for historical volatility is:

Zeta is the market value of an option, less its model value using the at-the-money implied volatility for the same expiration. It is a measure of the importance of using the volatility smile, rather than only ATM volatility. A nice dictionary of derivatives terms can be found at http://www.margrabe.com/Dictionary.html.

Source: Howard Savery, "Quantifying Volatility Convexity," Derivatives Strategy, 2/2000, pp. 54-55.

What you have described is the phenomenon of delta. Delta is defined as the ratio of the theoretical price change of the option to the price change of the underlying stock. The rule of thumb is that an at-the-money option has a delta of approximately 50%. Since your call option was right at-the-money when you bought it, for each $1 that the stock went up your option increased by 50 cents. As the stock continued to increase, so did the value of the option, but ALWAYS AT A SLOWER RATE THAN THE STOCK.

At some point the delta of your option approached 100% and it began to move at the same rate as the stock. But during that time, the movement of the stock outpaced that of the option by $6.40, the amount of your premium. If the stock fell back toward $20 the process would reverse itself and you would see some time value premium reappear.

The put-call ratio is simply the number of puts traded divided by the number of calls traded. It can be computed daily, weekly, or over any time period. It can be computed for stock options, index options, or future options. Some market technicians suspect that a high volume of puts relative to calls indicates investors are bearish, whereas a high ratio of calls to puts shows bullishness.

Many market technicians find the put-call ratio to be a good contrary indicator, meaning when the ratio is high, market bottom is near, and when the ratio is low, a market top is imminent. The more highly traded options contracts produce a more reliable put-call ratio. Traders and investors generally buy more calls than puts where stock options are concerned. Therefore, the equity put-call ratio is a number far less than 1.00. If call buying is heavy, the equity put-call ratio may dip into the .30 range on a daily basis. Very bearish days may occasionally produce numbers of 1.00 or higher. An average day will produce a ratio of around .50 - .70.

Once again, the numbers are interpretive numbers. Here are some numbers that may be used for illustrative purposes:

Index P/C Ratio

• Bullish: 1.5 or higher
• Bearish: .75 or lower
• Neutral: .75-1.5

Equity P/C Ratio

• Bullish: .75-1
• Bearish: .4 or lower
• Neutral: .4-.6

Put/Call ratio information can be obtained by going to Daily Put/Call Ratio or the Volume Query on OCC's web site.

The basic idea behind skew is that options with different strike prices and different expirations tend to trade at different implied volatilities. When implied volatilities for options with the same expiration are plotted, the graph resembles a smile, with at-the-money volatility in the middle and out-of-the-money options forming the gently-rising sides. As options go into the money they gradually approach their intrinsic value, and an option trading at its intrinsic value has an implied volatility of zero, so for our graph we use call prices for strikes above the current underlying stock price and put prices for strikes below the current underlying stock price.

There is a mathematical reason that skew appears as the "volatility smile" described above: most option pricing models assume stock prices are log-normally distributed, but in the real world stock prices deviate slightly from that model. Specifically, the Normal Distribution underestimates the probability of extremely large moves. In order to compensate, traders 'tweak' their models by using a higher volatility for out-of-money options.

But the skew also holds valuable information. An investor who takes the time and effort to carefully analyze the skew of a stock’s options can gain important insights into how the market is pricing risk. In some cases, for example, the perceived downside risk may be greater than the perceived upside risk, which causes the graph to be more of a 'smirk' than a 'smile.'

A measure of the rate of change in an option's theoretical value for a one-unit change in the price of the underlying stock.

For example if the delta of a call option is 50 (or .50 to be more precise), for each one point move in the stock, the anticipated movement of the option would be a half point - or 50%.

(The delta would be described in negative percentages for puts as the movement is opposite.)

Delta is one of the options greeks that is derived from an option pricing module. Delta, normally expressed as a percentage, seeks to measure the rate of change in an options' theoretical value for a one-unit (i.e. $1) change in the price of the underlying security or index. There are a couple of ways to obtain the "delta" of an option.

• From the OptionsEducation.org homepage, you can click on the menu link titled "Quotes". Enter a symbol and under "Apply to:", select "Detailed Options Chains." The option's Greeks (including the delta), will be listed in the table below.
• You can also solve for the option delta using our options calculator. There is an Options Calculator under the "Tool and Literature" link on our website. This calculator is available in Basic, Advanced, or Cycles format. First time users are encouraged to review the Basic calculator as there are discussions on the various inputs necessary to calculate an options' theoretical pricing.

Unless the underlying security is part of the penny pilot program, minimum increments for premiums below $3.00 are quoted in nickel (.05) increments. Premiums for $3.00 and above are quoted in dime (.10) increments. In reference to the question, a correct limit order price might be either $3.10 or $3.20. To read more about options quoting in penny increments, refer to this FAQ.

Yes – and you can read the current Options Listing Procedures Plan (OLPP) here: http://www.theocc.com/clearing/industry-services/olpp.jsp

When a stock closes below three dollars per share, the option exchanges are prohibited from adding new months and strikes. However, because Lucent recently closed above three dollars per share the exchanges were permitted to add new series. Lucent options are also part of the $1 strike pilot program.

Follow this link for a list of available series and strikes.

The "opening price" is simply the first reported trade in the option contract in question. You have to be careful, though. It's quite possible that the first trade of the day could take place 3 seconds, 10 minutes, 30 minutes or even an hour after the opening bell. In some cases, an option contract might not trade for several hours, days or even weeks! Perhaps you're wondering when the opening QUOTE for an option contract can occur? If this is the case, the answer is that opening quotes can take place as soon as the underlying security has opened on a primary exchange during regular trading hours - after 8:30 a.m. Central Time.

FYI, Equity options trading hours are from 8:30 a.m. to 3:00 p.m. (Central Time). Options on Exchange-Traded-Funds (ETFs) that are based on a broad-based index will generally trade from 8:30 a.m. to 3:15 p.m. (Central Time).