User manual for original web-based implied volatility calculator

The easiest and perhaps best way to come up with volatility estimates for your financial forecasts is to extract implied volatility measures from option prices. Implied volatility is based, not on someone's subjective or biased opinion, but on the prices at which options actually trade in the marketplace. Hence, implied volatility measures represent market consensus views of likely future volatility.

If you have never calculated implied volatility before, the calculator, instructions and links on the home page should make it easy for you to do so.

If you're unfamiliar with how market volatility relates to option prices, Black-Scholes Made Easy takes you through a series of simulations that make the relationships easy to understand.

Open calculator

More fields and buttons mean less work
Before looking up the data for options in which you're interested, take a moment to survey the calculator.

At first glance, the calculator may look like a lot of work. It's not. The information required to calculate implied volatility goes in the fields near the bottom of the calculator. The fields and buttons at the top of the calculator make it easier for you to come up with the required information.

Select the option type: American or European
The calculator can extract implied volatility from American- and European-style options. European-style options are those that you can exercise only at maturity. American-style options are those you can exercise at any time up to and at maturity.

The calculator opens with European-style option selected and with its fields partially filled with sample data from a recent, near-the-money SPX option on the S&P 500. The SPX is a European-style option.

Choose your option-pricing model
The calculator opens with the Black-Scholes-Merton model selected. This model is designed for European-style options— like the SPX. Under certain circumstances, the Black-Scholes-Merton model can give wrong values for American-style calls. It generally gives wrong values for American-style puts.

To extract implied volatility from American-style options, you can use any of the three other models. They are all binomial models. On the rare occasion that one doesn't work, try another. In their value calculations, binomial models take into account the potential advantage of early exercise of the option.

For binomial models, enter binomial N
Click the circle next to one of the binomial models.

Practitioners generally set N somewhere between 30 and 50 time periods. Type in the N of your choice here.

The accuracy of a binomial model's calculations is, in part, determined by the number of time periods into which it divides the option's time to expiration. Also, an even number of time periods yields a higher implied volatility than does an odd number of periods.

Market symbol
Type in the option's market symbol or the market symbol of the underlying. The symbol is for your reference only. It will be displayed in calculation reports.

Current index or asset price
Tab to the field and type in the current market index or current asset price of the option's underlying.

Strike price
Tab to and type in your chosen option's strike price. The usual convention in calculating implied volatility is to use a strike price near the underlying's current index or asset price.

Call bid, call ask; put bid, put ask
Calculating implied volatility from a call and a put that have the same strike price and time to expiration should give you the same implied volatilities— or values that are very close to one another.

Hence, entering price data for both a call and a put gives you an easy check on your data and on the model's calculations. To provide this quick check, the calculator asks for bid and ask prices on both calls and puts.

When working from market prices, the convention is to use as the option price the average of bid and ask prices. Click the Calculate Bid-Ask Averages button. Notice that the calculator puts the averages of the bid-ask prices into the call- and put-price fields. If you wish, you can tab to those fields and change the prices.

Start date, expiration date, and time to expiration
To calculate implied volatility, the calculator needs to know the options' time to expiration.

The calculator opens with today's date (from your computer) filled in as the option's start date. If you are doing calculations from some other as-of date, enter that date here.

When you look at an option's pricing data, it generally gives you the expiration year and month. It does not give you the expiration day. Every option expires on a given day of its expiration month— usually the Saturday immediately following the third Friday of the expiration month.

To find the Saturday immediately following the third Friday of the expiration month, type in the expiration year and month. Click Find Sat after Third Fri.

To find the number of calendar days between the option's start date and expiration date, click Find days to expiration. When you do, the calculator fills in the number of days to expiration.

While many options expire on a Saturday, no trading may take place on that day. Hence, the preceding day may be the effective expiration date. If that is the case, you may wish to decrease by one the calculated number of days to expiration.

Days/Year
To calculate the option's time to expiration, the calculator divides the number of days to expiration by the number of days per year.

If you're working with options that have long times to expiration, it's easiest to count calendar days and use 365-day years. If, however, you're working with options that have short times to expiration, you may want to work with trading days and a 252-day year. For a discussion of the implications of your choice, work through the simulations that go with page 117 of Black-Scholes Made Easy.

The calculator, however, does not count trading days. If you use trading days, you'll have to count them yourself and enter them in the Days to Expiration field. (The latest web version of the calculator and the desktop version count trading days.)

If, to count trading days, you want to see a calendar of the start month or expiration month, click one of those buttons. If you want to see calendars from the start month through the expiration month, click the Start - Exp Calendar button.

To make a calendar go away, click its button again.

From Simple Percent to Continuously Compounded Risk-free Rate
Option-pricing models require that we enter the current continuously compounded risk-free rate. As the risk-free rate, we can use the interest rate on a U.S. government bill or bond of a maturity that is equal to or close to the option's time to expiration.

Most sources quote interest rates as simple percents. Enter the simple percent in the top box. Click Calculate CC Equivalent and the calculator puts the continuously compounded rate in the bottom box.

Dividends
Some stocks pay dividends. The stocks that comprise some market indices pay dividends. The introduction of dividends on an underlying lowers the value of a call on that underlying and raises the value of a put. Accordingly, if an underlying pays dividends and, when you calculate implied volatilities, you leave the dividends out, the call and the put will give you different volatilities. Both will be wrong. The call price will give an implied volatility that is too low. The put price will give an implied volatility that is too high.

To see why the introduction of dividends lowers the value of calls and raises the value of puts, run the Black-Scholes Made Easy simulations that go with pages 89 - 95 of the book.

While many people ignore dividends in their options calculations, doing so is theoretically incorrect and may have practical consequences.

For lumpy dividends, a dividend schedule
Click Display Dividend Schedule. The dividend schedule opens with some example dividends filled in.

If you're working with an option on a stock that pays periodic dividends, enter in the schedule the amounts of the dividends during the option's time to expiration and the dates that the underlying goes ex-dividend.

After you enter a page of dividends, click Calculate net present value from dates.

If you happen to be working with trading days instead of calendar days, instead of entering ex-dividend dates, fill in the number of days until each ex-dividend date and click Calculate net present value from days to ex-div.

Close the dividend schedule.

Dividend Yield
If the stocks that comprise a market index pay dividends, the modeling convention is to treat those dividends collectively as a dividend yield on the underlying. When an index pays a dividend yield, click Enter Dividend Yield. At the bottom of the dividends column, enter the continuous dividend yield.

No Dividends
If the underlying pays no dividends, click No Dividends.

Calculate Implied Volatilities
When you click the Calculate Implied Volatilities button, the calculator calculates implied volatilities from both the call price and the put price. It displays the two volatilities and the difference between them.

If the difference is small, be happy. If large, ask why.
If the difference between the volatility calculated from the call and the volatility calculated from the put is small, then you are finished with the calculation. The small difference should give you more confidence in your results than if the difference between the two calculations is large.

In the marketplace, the put option commands a risk premium. Therefore its market price produces a higher implied volatility. If you want to go into the insurance business and earn insurance premiums, you can sell naked puts. You'll either earn a steady income or be wiped out.

What does that backwards arrow < thingee do?
Oh yeah, that < between the difference box and the copyright: While the calculator is laid out to calculate implied-volatilities from option prices, for no extra charge you also can go the other way. You can calculate option values from volatilities.

Instead of entering a call price, enter the underlying's expected volatility in the Vol from Call box. Instead of entering a put price, enter the underlying's expected volatility in the Vol from put box.

Click <.  

The model's theoretical values appear in the Call Price and Put Price boxes.

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