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1The Smile in Option PricesWhen option prices are well described by the Black-Scholes model, then when we examine the prices of a set of options on the one asset with a common maturity date and different exercise prices they will all have the same implied volatility.• Suppose S= $65; X= $65; t= 1/4 year (3 months); continuously compounded risk-free rate r= 9.53102% p.a. • Suppose the option is trading at $5.285407.⇒If the market is using Black-Scholes, then its estimate of the volatility of the stock is 35% p.a.; i.e., σ= 0.35.ln()(). . .2rt12121SrtX2cSN deXN ddddttσσσ−++=−≡≡−
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