The CBOE Volatility Index - VIX

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  • Topic: Option, Call option, Chicago Board Options Exchange
  • Pages : 14 (4547 words )
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  • Published : March 3, 2013
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Table Of Contents:
Uses of VIX12
Investor Fear Gauge:12
Hedging with VIX:13
Hedging with VIX Options and Futures:15
Risk management case study application:16

The VIX is the ticker symbol for the volatility index that the Chicago Board Options Exchange (CBOE) created to measure the implied volatility of options on the S&P 500 index (SPX) over the next 30 calendar days. The formal name of the VIX is the CBOE Volatility Index. Originally, it was pioneered by Professor Robert Whaley in 1993. In the same year CBOE introduced Volatility Index that measured market’s expectation of 30 day volatility implied by eight at-the money S&P 100 (OEX) put and call option prices. Throughout a decade VIX gained popularity and recognition in the capital market especially in the US. In 2003, CBOE together with Goldman Sachs reviewed and updated VIX which is based on a broader index S&P 500 (SPX) one of the main indexes of U.S. equities. The new VIX estimates the expected volatility for next 30 days by averaging weighed price of SPX puts and calls option over wide range of strike price. VIX is commonly referred as Fear Gauge or Fear Index because it is said to be a good indicator of the level of fear and greed of investors in the U.S. on the equity market. When there is a fear among investors, the VIX level is notably higher than normal. The ratio of VIX to S&P 500 during our economic crisis of 2008 clearly underlines this property as demonstrated in graph 1. This strong negative correlation will be examined later in the report and brings the second use of this product, hedging. (CBOE, 2009) Graph 1:

Today VIX has established itself from abstract concept to standard use that many market participants find it practical. CBOE introduced the first exchange-traded VIX futures contract in March 24, 2004. After two years time, CBOE also launched VIX options. These financial products are very successful. (CBOE, 2009) Within 5 years volumes of VIX options and futures has grown to more than 100,000 contracts a day as supported by graph 2. They have become highly liquid and both have also received award for most innovative index derivative product. Graph 2:

VIX is a Volatility Index consists of options rather than stocks. The original VIX which was introduced in 1993 (which was based on Black Scholes Formula) is calculated slightly different than the new VIX that is currently in use. New calculation (not based on Black Scholes) differs from the former by two main respects: it is based on S&P 500 rather than S&P 100 (S&P 500 gives more accurate view of investors' expectations on future market volatility); and it utilizes broad range of strike prices rather than at-the-money option prices. Calculation of VIX involves rules for selecting component options and a formula to calculate the index values. (Whaley, 2008)

Generalized formula used in the VIX calculation

σ^2=2/T ∑_i▒(〖∆K〗_i/(K_i^2 ) e^RT Q(K_i)) -1/T [F/K_0 -1]^2 Where
σVIX/100 => VIX= σ * 100
T Time to expiration
F Forward index level derived from index option prices
K_0 First strike below the forward index level, F
K_i Strike price of i^(th) out-of-the-money option; a call if K_i >K_0 and a putif K_i < K_0; both put and call if K_i =K_0 〖∆K〗_i Interval between strike prices – half the difference between the strike on either side of K_i 〖∆K〗_i=(K_(i+1)-K_(i-1))/2

(Note: ∆K for the lowest strike is simply the difference between the lowest strike and the next higher strike. Likewise, ∆K for the highest strike is the difference between the highest strike and the next lower strike.)

R Risk free interest rate
Q(K_i) The midpoint of the bid-ask spread for each option with strike K_i

VIX is a measure of expected volatility of SPX for the next 30 days. Calculation uses two options: near term and next term put and call options usually in the first and second...
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