VIX - THE FEAR INDEX

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VIX - THE FEAR INDEX

• Stephen Perno
• Kaitlin Cherundolo

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What is VIX?

• VIX ticker symbol for Chicago Board Options
  Exchange Volatility Index
• VIX Measures
• Market expectations
• Expected Movement in the SP 500
• Correlation between high value of VIX and market
  volatility
• Relation to high option prices

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History of VIX

• The original VIX
• Based on SP 100 Index option prices
• Extracted implied volatilities from
  option-pricing model (BlackScholes, etc.)
• Constructed using implied volatilities of 8
  different option series
• 1993 - The new VIX Index was introduced in a
  paper by Professor Robert E. Whaley of Duke
  University

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History of VIX

• December 24, 1993 - The VIX's lowest recorded
  value (between 1990 and 2008)
• 2003 - The underlying index is changed from the
  CBOE SP 100 Index (OEX) to the CBOE SP 500
  Index (SPX).
• Estimates expected volatility from option prices
  in wide range of strike prices, not just
  at-the-money strikes as in original VIX

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History of VIX

• March 26, 2004 - Trading in futures on the VIX
  Index began.
• February 2006 - VIX options were launched in.
• October 24, 2008 - VIX reached an intraday high
  of 89.53.
• Between 1990 and October 2008, the average value
  of VIX was 19.04

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How Is VIX Calculated?

• Old VIX calculated from Black Scholes option
  pricing model
• Uses a newly developed formula to derive expected
  volatility by averaging the weighted prices of
  out-of-the money puts and calls
• Independent of any model

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Generalized Formula for VIX

• Where
• s VIX/100
• ? VIX 100s
• T maturity
• F forward index level derived from index prices
• Ki strike price of i-th out-of-the-money
  option
• call if Ki gt F
• put if Ki lt F

• ?Ki interval between strike prices half the
  distance between the strike on either side of
  Ki
• K0 first strike below forward index level, F
• R risk-free interest rate
• Q(Ki) midpoint of bid-ask spread for each
  option with strike Ki

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Interpreting the Numbers

• If VIX 23,
• Expected change of 23 of the SP Index over 30
  days (annualized) OR
• Up and down movement in the SP OR
• Index options priced with a 68 chance that SP
  500s 30-day return lt 6.64.

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Why Is It Called the Fear Index?

• VIX is a measure of fear of volatility in either
  direction
• Investors believe
• High value of VIX translates into a greater
  degree of market uncertainty
• Low value of VIX is consistent with greater
  stability
• When investors anticipate large upside
  volatility, they are unwilling to sell upside
  "call" stock options unless they receive a large
  premium

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And Now to Excel
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Comparison of Original VIX, New VIX, and SP 500
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Example Long Term CapitalManagement and Russian
Debt Crises in 1998
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Correlation Graph for VIX and SPX
Note Negative slope implies negative
correlation between VIX and SPX.
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VIX-based Derivative Instruments

• VIX futures contracts, which began trading in
  2004
• Exchange-listed VIX options, which began trading
  in February 2006

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Critiques of VIX

• VIX measures index option volatility over 30 days
  when equity options have 2-6 month maturities
• Volatility usually high in technology stocks, and
  low in utility stocks
• So, VIX may be too simplistic to estimate for all
  types of stocks

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So, Does VIX Predict the Future?!?

• Given what we have seen
• Correlation YES
• Predictor NO?

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Addendum Other Volatility Indexes Beyond VIX

• Nasdaq-100 Volatility Index (VXN)
• DJIA (VXD)
• Russell 2000 (RVX)
• SP 500 3-Month (VXV)
• Commodities and Foreign Currencies
• Crude Oil (OVX)
• Gold (GVZ)
• EuroCurrency (EVZ)

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Bibliography

• http//en.wikipedia.org/wiki/VIX
• http//www.cboe.com/micro/vix/vixwhite.pdf
• http//www.riskglossary.com/link/spreads.htm
• http//finance.yahoo.com (DOW, SP500, and VIX)