Consider a stock worth $40 that can go up or down by 10% per period. The risk-free rate of interest is 6% pa, continuously compounded.

(i) Determine the intrinsic values at expiration of a one-year European call option

with an exercise price of $40. Show the binomial tree.

[10%]

1. (ii)Using the risk neutral valuation, find the current value of the option.
2. (iii)Construct a hedge by combining a position in stock with a position in the call. Show that the return on the hedge is the risk-free rate regardless of the outcome, assuming that the call sells for the value you obtained in part (ii).
3. (iv)Determine the rate of return from a riskless hedge if the call is sold for $5

when the hedge is initiated.