Risk neutral heshe risk neutrality is critical for

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Unformatted text preview: he example We because S&P500 index is very diversified and may serve as a good proxy for the underlying assets for the representative risk-neutral investor (the S&P 500 reflect the wealth of the whole market, so if the investor owns the whole market, he/she is rich enough for being risk-neutral) he/she Risk-neutrality is critical for the risk-free world Risk-neutrality assumption assumption 15-22 A real example – S&P 500 option (2) – On Oct. 28, 2011, S&P index is at 1,285.09 15-23 A real example – S&P 500 option (3) Now, let’s check the call option price of SP500 Now, matures on Nov. 18, 2011 (15 trading days to go) matures We pick the most liquid call options (close to We current stock price) current 15-24 A real example – S&P 500 option (3) We use the past one-year S&P 500 index return We to estimate the daily average return on the S&P 500 index The daily average return can be regarded as the “risk-free rate” because it “could” reflects the expected returns on a risk-free asset (i.e., S&P 500) in a risk-free world (this is just a simplification, though) simplification, As you can see in “SP500daily”, the average As daily return on the S&P 500 over the past year is 0.000415, and the standard deviation = 0.01343 0.000415, 15-25 A real example – S&P 500 option (4) We let dividend yield = 0%, current stock price We =1285.09, and number of steps = 100 =1285.09, We find that all considered call options provide We an estimate of daily volatility at 1.1%, which is slightly lower than the past year (1.3%) Strike CallOptionPrice Implied volatility 1275 30.5 1.1% 1280 28.19 1.1% 1285 25.29 1.1% 1290 22.5 1.1% 1295 19.67 1.1% 1300 16.8 1.1% 15-26 A real example – S&P 500 option (5) We pick the most liquid put options (close to We current stock price) current 15-27 A real example – S&P 500 option (6) We find that all considered put options provide an We estimate of daily volatility from 1.5%-1.6%, which is higher than the past (1.3%) Strike CallOptionPrice Implied volatility 1275 22.8 1.6% 1280 25.5 1.6% 1285 27.05 1.6% 1290 29.5 1.6% 1295 30.8 1.5% 1300 33.5 1.5% 15-28 VIX: An index for S&P 500 volatility – VIX is the ticker symbol for the Chicago Board VIX Options Exchange Market Volatility Index, a popular measure of the implied volatility of S&P 500 index options. http://en.wikipedia.org/wiki/VIX 500 15-29...
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This document was uploaded on 03/03/2014.

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