10b Multiperiod Options - Princeton University

Fin 501:Asset pricing IFin 501:Asset pricing ILecture 10: MultiLecture 10: Multi--period Modelperiod ModelLecture 10: MultiLecture 10: Multiperiod Modelperiod ModelOptions Options BlackBlack--ScholesScholes--Merton modelMerton modelProf. Markus K. BrunnermeierProf. Markus K. Brunnermeier1 Fin 501:Asset pricing IFin 501:Asset pricing IBinomialBinomialOptionPricingOptionPric ingBinomial Binomial Option PricingOption pricing Consider a European call option maturing at time T ihikKC(SK0)hfliwith strike K: CT=max(ST K,0), no cash flows in betweenNtblttti llli tthiffijt Not able to statically replicate this payoff using just the stock and risk free bond Needtodynamicallyhedgerequiredstock Need to dynamically hedge required stock position changes for each period until maturity statichedgeforforwardusingput callparitystatic hedge for forward, using putcall parity Replication strategy depends on specified random process of stock price

Fin 501:Asset Pricing I Risk‐neutral probabilities • Note that p is the probability that would justify the current stock price S in a rikisk‐neutral world: []quS q dS R S = +(1− ) 1 p u d R d q = − − = • No arbitrage requires u > R > d as claimed before

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  University, Princeton, Princeton university, Pricing, Arbitrage, 10b multiperiod, Multiperiod

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