European call option Sample Clauses

European call option. The rescaled payoff function for a European call option is Λ¯ (z) = max{ez − 1, 0}. Then v(x, τ ) = e−rτ ∫ ∞ 1 e−(x−z−( 1 σ2−r)τ )2/(2σ2τ ) (ez − 1) dz. (3.19) 0 √ 2πσ2τ This can be integrated. Finally, we get the exact solution for the European call option c (S, t) = SN (d1) − Ee−r(T −t)N (d2), where (3.20) N (y) = 1 y ∫ √ 2 z e− 2 dz, (3.21) 2π −∞ √ log( S ) + (r + 1 σ2)(T − t) d1 =

European call option. The rescaled payoff function for a European call option is Λ¯(z) = max{ez − 1, 0}. Then