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**Unformatted text preview: **= 1/√2π S σ √dt ≈ 0.4 x S 0 σ√dt d) Estimate the fair value of a 1-week at-the-money call on the S&P 500 index using the following data: S&P 500 spot price: 2000 S&P 500 volatility: 20% HWASSGN #9 EXERCISE HW 9-3. Consider a call opton on ABC Inc. wiTh The following informaton: STrike price $1 MaTuriTy: 1 yearVolatliTy: σ InTeresT raTe: 0% No dividends LeT c(S) be The Black-Sholes call value as a functon of ABC Inc’s spoT price S. a) show ThaT SN’ (d 1 ) = N’ (d 2 ) where N’ (x) = e –x2/2 / √2π is The sTandard normal partal disTributon densiTy functon and d 1 = ln S + σ 2 /2, d 2 = d 1 – σ. /σ b) Carefully show ThaT c’ (S) = N (d 1 ) where N(.) is The sTandard normal cumulatve disTributon functon. c) Assuming σ = 30% calculaTe c’ (1) and inTerpreT This number using a FrsT-order ±aylor series expansion, wiTh emphasis on Fnancial inTerpreTaton. d) Assuming σ = 30% produce a graph of c’ (S) for 0 < S ≤ 2....

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- Spring '14
- SamirEl-Gazzar
- Normal Distribution, Volatility, Probability theory, probability density function, Cumulative distribution function, ABC Inc., cash position