A European put option written on stock has strike price $10 and expires at time t = 1. At the current time t = 0 the underlying stock has price S(0) = $9 and at expiry the price will be either S(1,) = $11 or S(1,) = $7. The interest rate over t = 0 to t = 1 is r = 1/5 .

(a) Show that there is no arbitrage opportunity.

(b) Construct a replicating portfolio for this put option. Calculate H0 and H1 (as dened in lectures) for this replicating portfolio and thus nd the value of the put at the current time P(0), correct to four decimal places

(c) You should find that Ho is positive and H1 is negative. What does this mean?

(d) Check your solution for P(o) by calculating the risk neutral probabilities and using the general pricing formula.