The black's model: Payoff Later 22.8 Than Variable Being Observed c=P(O, T[FON(d-KN(d2) p=P(0,T)KN(-a2)-F0N(-d1) n(F/K)+27/2 T K: strike price °T: time when Fo forward value of variable is observed variable T*: time of payoff °σ: volatility Options, Futures, and other Derivatives, 5th edition 2002 by John C. HullOptions, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull The Black’s Model: Payoff Later 22.8 Than Variable Being Observed • K : strike price • F0 : forward value of variable • s : volatility • T : time when variable is observed • T * : time of payoff d d T T F K T d p P T KN d F N d c P T F N d KN d = −s s + s = = − − − = − 2 1 2 0 1 2 0 1 * 0 1 2 * ; ln( / ) / 2 (0, )[ ( ) ( )] (0, )[ ( ) ( )]