The Binomial Tree

Terminal Payoffs

A terminal option payoff is computed at each final stock node.

highlighted = computed this step

Call strike

At expiry, a call with strike $105.00 pays the maximum of stock minus strike and zero.

call payoff=max⁡(S−K,0)\text{call payoff}=\max(S-K,0)
Two-period binomial treeThe recombining stock tree and call values are recomputed.updowntodayS $100.00V $5.67t1 u0S $90.00V $1.00t1 u1S $120.00V $15.00t2 u0S $81.00V $0.00t2 u1S $108.00V $3.00t2 u2S $144.00V $39.00

Terminal payoffs

The call pays $39.00 at the all-up stock price, $3.00 at the recombined middle stock price, and $0.00 at the all-down stock price.

Vuu=$39.00,Vud=Vdu=$3.00,Vdd=$0.00V_{uu}=\$39.00,\quad V_{ud}=V_{du}=\$3.00,\quad V_{dd}=\$0.00

Option payoff link

This is the same call-payoff rule applied separately at each terminal stock node.

V=max⁡(S−K,0)V=\max(S-K,0)