Question $4$

A stock worth $$25$ that can go up or down by $15$ percent per period. The risk$-$free rate is $10$ percent. Use one binomial period.

a$.$ Determine the two possible stock prices for the next period.

b$.$ Determine the intrinsic values at expiration of a European call option with an exercise price of $$25.$

c$.$ Find the value of the option today.

d$.$ 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 c$.$

e$.$ Determine the rate of return from a riskless hedge if the call is selling for $$3\mathrm{.}50$ when the hedge is initiated.