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.todaydownupS $100.00V $10.20S $90.00V $1.43S $120.00V $20.00S $81.00V $0.00S $108.00V $3.00S $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. The payoff values are model payoffs from the stated strike and terminal stock prices, not market prices or forecasts. This is descriptive, not investment advice.

V=max⁡(S−K,0)V=\max(S-K,0)