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Unformatted text preview: • Investor writes one call and buys H shares of underlying stock • If price goes up, will be worth uHSC u • If price goes down, worth dHSC d • For what H are these two the same? Binomial Option Pricing Formula • One invested HSC to achieve riskless return, hence the return must equal (1+ r) ( HSC ) • (1+ r )( HSC )= uHSC u = dHSC d • Subst for H , then solve for C BlackScholes Option Pricing Call T the time to exercise, σ 2 the variance of oneperiod price change (as fraction) and N(x) the standard cumulative normal distribution function (sigmoid curve, integral of normal bellshaped curve) =normdist(x,0,1,1) Excel (x, mean,standard_dev, 0 for density, 1 for cum.) BlackScholes Formula Actual S&P500 Volatility Monthly July1871 April 2008 Implied and Actual Volatility Monthly Jan 1986April 2008...
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 Spring '08
 RobertShiller
 Economics, Normal Distribution, Options, Mathematical finance, Prof. Robert Shiller

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