The possible movement in share price over the next 12 months is depicted in the 4-step Binomial tree shown below.

Key details are:

the proportional up and down movements on each branch of the tree are u = 1.1912 and d = 0.8395 respectively

the riskfree interest rate is 4% pa continuously compounded

Let S_T denote the share value one year from now (far right side of the Binomial tree).

A strange derivative security is based on this share. It has a payoff = sqrt(S_T).

That is, if you buy this derivative today, one year from now you receive a payoff equal to the square root of whatever the share price is.

Required:

Using the 4-step Binomial tree, calculate the fair value of this derivative today.