A European call on this equity expires in period $2,$ and has a strike price of $21.$

So $=25$$ 

 

Su $=33$$ 

 

Sd$=13$$

Suu$=40$$

Sud $=20$$

Sdd $=10$$

The risk$-$free rate is $5$ percent from date $0$ to date $1,$ and $4$ percent from date $1$ to date $2.$

a$)$ Calculate the risk$-$neutral probabilities implied by the binomial tree.

b$)$ Calculate the pay$-$offs of the call option at each of the three nodes at date $2.$

c$)$ Calculate the value of the call at date $0.$