Technical Information


Volatility literally represents the standard deviation of day-to-day price changes in a security, expressed as an annualized percentage. We commonly use two measures of volatility in options trading: historical and implied. Historical volatility depicts the degree of price change in an underlying security observed over a specified period using standard statistical measures. It is not a forecast of future volatility. Implied volatility is the market's prediction of expected volatility, calculated indirectly 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 at-the-money volatility.



I am perplexed when the option premium disappears from my options. I paid $6.40 for a 20 strike call with two years until expiration when the stock was trading at $20 per share. Now the stock is above $50, but the premium has totally disappeared. The option still has 18 months to expiration and I don’t understand why the premium went away so quickly. It seems like I lost $6.40 somewhere.

What you have described is the phenomenon of Delta. We define Delta 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 $0.50. As the stock continued to increase, so did the value of the option, but at a slower rate than the stock.

At some point, the Delta of your option approached 1.00 and it began to move at the same rate as the stock. However, 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. We can compute it for stock options, index options or futures options on a daily, weekly, or annual basis. 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.

Other market technicians find the put-call ratio to be a good contrary indicator. This means that 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 you can use for illustrative purposes of the contrarian view:

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

Obtain put/call ratio information by going to Daily Put/Call Ratio or the Volume Query on OCC's website.



The basic idea behind skew is that options with different strike prices and different expirations tend to trade at different implied volatilities. When we plot implied volatilities for options with the same expiration, 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. Therefore, 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.

However, the skew also holds valuable information. An investor who takes the time and effort to 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 premium would be $0.50.

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



Delta is one of the options Greeks derived from an option-pricing model. Delta 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, select the menu link titled Options Quotes in the Tools & Resources section. Enter a symbol and click ‘Go’ to view a 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 Tools & Resources tab 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 option's theoretical pricing.



I tried to enter a limit order to buy an option for $3.15. My order was rejected due to entering an incorrect price. What was wrong with the price I entered?

Unless the underlying security is part of the penny pilot program, minimum increments for premiums below $3 are quoted in $.05 increments. Option premiums that are $3 or more are quoted in $.10 increments. Different exchange programs allow for option premiums to trade in other ways beyond the standard method. In reference to the question, a correct limit order price might be either $3.10 or $3.20.

Also, certain brokerage houses’ trading platforms may be limiting the prices at which orders can be sent.



Listing information is available in the current Options Listing Procedures Plan (OLPP) on the OCC website.

You can also view a list of available series and strikes.



How is an equity options' opening price determined? Does the market maker or specialist set it prior to the market open? Is it based on the first trade of the day?

The opening price is simply the first reported trade in the option contract in question. You have to be careful, though. It's 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. Maybe 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 opens on a primary exchange during regular trading hours, after 8:30 a.m. CT.

Equity options trading hours are from 9:30 a.m. to 4:00 p.m. ET (8:30 a.m. to 3:00 p.m. CT). Options on exchange traded funds (ETFs) based on a broad-based index generally trade from 9:30 a.m. to 4:15 p.m. ET (8:30 a.m. to 3:15 p.m. CT).