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 risk-free interest rate is 4% pa continuously compounded

Let ST 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(ST).

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.

Give your answer to at least 2 decimal places.

80 Node Time: 0.0000 95.30 67.16 0.2500 113.53 80 56.38 0.5000 135.24 95.30 67.16 47.32 0.7500 161.10 113.53 80 56.38 39.73 1.0000