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The FEAR Gauge

An Introduction to theVolatility Index

by Amy Ackers

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Brief OverviewWhat is the Volatility Index?

Market tool forinvestors

Def: Index of implied volatility of eight

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

Ticker symbol is VIX

Continuously quoted throughout each tradingday

Provides accurate estimate of short term stock

volatility

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The1987Stock Market Crash Dow Jones Industrial Avg. fell 508 points

(22.6% drop)

Largest one day drop in Stock MarketHistory

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

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Aftermath of Black Monday

Reports state that derivatives market heavilyaffected the stock crash

Investors saw the dangers of naked put/calloptions (infinite gains and losses)

Faith in Options Market vanishes

CFTC Report - Massive Change in investorperception.

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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 FEARGAUGE 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 OEXindex

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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 almostany stock that contains options

Implied Volatility - Combination of supply anddemand, along with the investors estimates. Allows

options to be compared in accordance with sixvariables. It uses current market values to becalculated. Lets look closer ...

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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

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Implied Volatility Cont...

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

Rewrite the appropriate valuation modelwhere the Option Price is known and thevolatility is being solved for

Option price value comes from the mid-pointof actual bud/ask prices in the current market,and therefore the volatility is implied by thisOption Index Stock Price

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Implied Volatility Cont...

All stock options (and implied volatilities) used in thecurrent options market are priced using a variation ofBlack-Scholes Formula.

Black-Scholes Equation components Current stock price - Time of expiry

Option exercise price - Risk free interest rate

volatility (only unknown variable)

dividends2

2 2

2

10

2

V V VS rS rV

t S S

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Implied Volatility Cont...

Example : The normal use of this equation would be toprice a Call Option, C, where all other variables in theequation 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 solvingfor s, taking our value of C from the OEX IndexOption Price

This generates a value of Implied Volatility

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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 stockoptions

Ticker Symbol (OEX)

Houses over 240,000 contracts

The constituent companies are leaders in theirrespective industries, actively trade equityoptions, and have a very liquid share base

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Eight Call/Put Options

VIX is constructed of eight near-the-money andsecond-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 toexpiration

Second-near-the-money : option prices of the nextadjacent month

Two different Exercise prices used (One just below

current OEX level, one just above current OEX level)

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Calculation of the VIX

Near-the-Money OptionsE1 = Exercise Price below currentvalue

E2 = Exercise Price above currentvalue

+ one call at E1

+ one put at E1

+ one call at E2+ one put at E2

Second-near-the-MoneyE1 = Exercise Price below currentvalue

E2 = Exercise Price above currentvalue

+ one call at E1

+ one put at E1

+ one call at E2+ one put at E2

Eight Option Prices in Total

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Calculation of the VIX

Calculate the Implied Volatilities of the eight Put/Calloptions on the OEX index

Average the Implied Volatilities within four separatecategories 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 impliedvolatilities to get an At-the-money volatility avg

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Calculation of the VIX

Final Step:

Plug in calculated Volatilities into the VIX

equationVIX = 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 nearN2 = # 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)

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How is the VIX Used?

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

More simply, a high VIX shows a greater riskin the market, whereas a low VIX shows astable 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

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How is the VIX Used?

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The VIX as a Forecaster

Along with predicting marketdrops, the VIX acts as an indicator

of fair priced options A high VIX implies that option

prices are expensive incomparison to historical prices

A low VIX indicates that optionprices are cheap in comparison tohistorical prices

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Developed Strategies

Most reliable strategies with short term stockoptions

An increasing VIX means the stock market is

experiencing large, traumatic declines, whichis a signal for buying opportunities. Purchase Deep-in-the-money calls or sell both calls

and puts

Declining VIX means stock market is stableand it is virtually impossible to predict futurechanges Purchase of puts is least risky strategy

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Future of the VIX

Using the methodology as the VIX, the CBOEhas 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

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Questions????