Short sell a risk free bond with face value k and

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Unformatted text preview: folio A’s payoff at T is ST – K Portfolio B: Portfolio 1. Buy 1 share of the stock that is of price S now (the current price is S ) 2. Short sell a risk-free bond with face value K and will rT matures in T (the current price is K e--rT ) 3. Portfolio A’s payoff at T is ST – K 15-7 BS model in excel (no dividend) • See “BS model” • See “BS VBA” 15-8 Black-Scholes model for European options (with dividend) 15-9 Black-Scholes model with dividends c = S e − qT N (d1 ) − K e − rT N (d 2 ) p = K e −rT N (−d 2 ) − S e −qT N (−d1 ) ln( S / K ) + (r − q + σ 2 / 2)T where d1 = σT ln( S / K ) + (r − q − σ 2 / 2)T d 2 = d1 − σ T = σT q = annualized continuously compounded dividend ratio qT qT S e--qT = The price of e--qT share of the dividend-paying stock (Why do we have to include e-qT? because we will because receive dividend until T) (i.e., our stock will “grow up” (i.e., to be one at time T) 15-10 See “BS_div” tab for a practice of option pricing Put-Call Pa...
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