Lecture Week 9B. The Smile in Option Prices(3).pdf

Lecture Week 9B. The Smile in Option Prices(3).pdf - The...

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1 The Smile in Option Prices When 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 ( ) ( ). . . 2 rt 1 2 1 2 1 S r t X 2 c SN d e XN d d d d t t σ σ σ + + =
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