The FEAR Gauge

An Introduction to the Volatility Index

by Amy Ackers

Brief OverviewWhat is the Volatility Index?

• Market tool for investors• Def: Index of implied volatility of eight

put/call options, near the money and second near the money, for two stated strike prices given by the S&P 100 Options Index (OEX)

• Ticker symbol is VIX• Continuously quoted throughout each

trading day• Provides accurate estimate of short term

stock volatility

The1987 Stock Market Crash

• Dow Jones Industrial Avg. fell 508 points (22.6% drop)

• Largest one day drop in Stock Market History

• Overwhelming Volume of Stocks exchanged (600 million shares per day)

• U.S. Stocks dropped over 30% ($1 trillion)• Chicago Board of Options Exchange (CBOE)

temporarily suspended trading in the OEX

Aftermath of Black Monday

• Reports state that derivatives market heavily affected the stock crash

• Investors saw the dangers of “naked” put/call options (infinite gains and losses)

• Faith in Options Market vanishes• CFTC Report - “Massive Change in

investor perception.”

Creation of the VIX

• Established in 1993 by the CBOE• Indexed investors’ feelings of stock option

risk levels in the S&P 100, making it the FEAR GAUGE of Investors

• Characteristics of the VIX– Index continually calculated throughout 9am-3pm CST trade

day– Represents implied volatility of a 22 trade day month for at-

the-money options of the OEX– Values derived from the mid-point of bid/ask prices of the

OEX index

Volatility: An Overview

• Volatility comes in two basic varieties: Historical Volatility - measure of standard

deviation of past daily returns during a specific time period . It is a published figure that can be found on almost any stock that contains options

Implied Volatility - Combination of supply and demand, along with the investors estimates. Allows options to be compared in accordance with six variables. It uses current market values to be calculated. Let’s look closer ...

Implied Volatility:WHAT IS IT?

• Y = 3x + 2 • Solve using X = 3 … we get Y = 11• But what if you were given the Y value ?• Work backwards and rewrite the

equation to solve for x…• X = (Y-2)/3• Given any Y , we can now solve for X

Implied Volatility Cont...

• To derive Implied Volatility, we use the same concept as in the Y = 3x + 2 equation

• Rewrite the appropriate valuation model where the Option Price is known and the volatility is being solved for

• Option price value comes from the mid-point of actual bud/ask prices in the current market, and therefore the volatility is “implied” by this Option Index Stock Price

Implied Volatility Cont...

• All stock options (and implied volatilities) used in the current options market are priced using a variation of Black-Scholes Formula.

• Black-Scholes Equation components– Current stock price - Time of expiry– Option exercise price - Risk free interest rate– volatility (only unknown variable)– dividends

22 2

2

10

2

V V VS rS rV

t S S

Implied Volatility Cont...

• Example : The normal use of this equation would be to price a Call Option, “C,” where all other variables in the equation have a set value C = S N(x1) - B N(x2) where...

x1 = log(S/B)/s + s/2 S = current stock price T = time to expiry

x2 = log(S/B)/s - s/2 B = Xexp(-rT) exercise price s = volatility

r = risk free interest rate

• For Implied Volatility we rewrite the equation solving for “s,” taking our value of “C” from the OEX Index Option Price

• This generates a value of Implied Volatility

OEX: S&P 100 Index

• Originated in 1983 by the CBOE• An index of the 100 largest blue chip

companies in the S&P 500 with listed stock options

• Ticker Symbol (OEX)• Houses over 240,000 contracts• The constituent companies are leaders in their

respective industries, actively trade equity options, and have a very liquid share base

Eight Call/Put Options

• VIX is constructed of eight near-the-money and second-near-the-money option prices (4 Calls/4 Puts) for the OEX stock price, where the OEX index IS the underlying asset.

• Near-the-money : option prices of the OEX with shortest time to expiration, but no less than 8 days to expiration

• Second-near-the-money : option prices of the next adjacent month

• Two different Exercise prices used (One just below current OEX level, one just above current OEX level)

Calculation of the VIX

Near-the-Money Options

E1 = Exercise Price below current value

E2 = Exercise Price above current value+ one call at E1+ one put at E1+ one call at E2+ one put at E2

Second-near-the-Money

E1 = Exercise Price below current value

E2 = Exercise Price above current value+ one call at E1+ one put at E1+ one call at E2+ one put at E2

Eight Option Prices in Total

Calculation of the VIX

• Calculate the Implied Volatilities of the eight Put/Call options on the OEX index

• Average the Implied Volatilities within four separate categories…– Near-the-money Calls -Second-near-the money Calls– Near-the-money Puts -Second-near-the money-Puts

• Interpolate between the near and second-near implied volatilities to get an At-the-money volatility avg

Calculation of the VIX

• Final Step: Plug in calculated Volatilities into the VIX

equation VIX = s1(N2-22)/(N2-N1) + s2(22-N1)/(N2-N1)

where s1 = near-the-money implied volatility s2 = second-near-the-money implied volatility

N1 = # of trading days left to expiration of “near” N2 = # of trading days left to expiration of “second”

• We have finally derived the Implied Volatility! (The single value given on the VIX index each day)

How is the VIX Used?

• Elastic Relationship: overall drop in the OEX returns produces a rise in returns of the VIX

• More simply, a high VIX shows a greater risk in the market, whereas a low VIX shows a stable market

• Historical values in VIX range from a high of 150 in 1987, to a low of 8 in 1993-4.

• Spikes in the VIX graph indicate drops in the market

• Present value of VIX : 19.62

How is the VIX Used?

The VIX as a Forecaster• Along with predicting market

drops, the VIX acts as an indicator of fair priced options

• A high VIX implies that option prices are expensive in comparison to historical prices

• A low VIX indicates that option prices are cheap in comparison to historical prices

Developed Strategies

• Most reliable strategies with short term stock options

• An increasing VIX means the stock market is experiencing large, traumatic declines, which is a signal for buying opportunities.– Purchase Deep-in-the-money calls or sell both

calls and puts

• Declining VIX means stock market is stable and it is virtually impossible to predict future changes– Purchase of puts is least risky strategy

Future of the VIX

• Using the methodology as the VIX, the CBOE has created the Nasdaq Volatility Index (VXN) based on the Nasdaq 100 index (NDX)

• Calculated every 60 seconds from 8:45am to 3pm CST

• Based on the same 22 trading day calendar as the VIX

• Newest benchmark for technology stock volatility

Questions????