Lecture6_BSmodel

# Portfolio as payoff at t is st k portfolio b

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Unformatted text preview: rity – with dividends (1) Portfolio A: Portfolio 1. Buy 1 unit (1 share) of call option at strike price K (the current price is c) 2. Sell 1 unit (1 share) of put option at strike price K (the current price is p) 3. Portfolio A’s payoff at T is ST – K Portfolio B: Portfolio 1. Buy e-qT share of the stock that is of price S now (the qT current price is S e--qT ) (Note that e-qT unit of stock will grow to 1 share of stock in T ) 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 15-11 Put-Call Parity – with dividends (2) Parity: Parity: - So, the cost of portfolio A and portfolio B should be the same (i.e., the premium of A – the premium of B = the current price of e-qT unit of the stock – the current price of the risk-free bond) the c − p = S e − qT − K e − rT since c = S e − qT N (d1 ) − K e − rT N (d 2 ) p = c − S e − qT + K e − rT = S e − qT N (d1 ) − K e − rT N (d 2 ) − S e...
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