The One-Period Model

A Derivative's State Payoffs

A derivative is specified by what it pays in each future state.

highlighted = computed this step

Call strike

A call with strike $105.00 pays the amount by which the stock finishes above the strike.

call payoff=max⁡(S−K,0)\text{call payoff}=\max(S-K,0)
Call payoff by stateA call payoff is recomputed from the strike and stock states.updownTodayS0 $100.00V0 $5.00Up stateSu $120.00Vu $15.00Down stateSd $90.00Vd $0.00

State payoffs

In the up state, the payoff is $15.00; in the down state, the payoff is $0.00.

Vu=$15.00,Vd=$0.00V_u=\$15.00,\quad V_d=\$0.00