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 defined in lectures) for this replicating portfolio and thus find the value of the put at the current time P(0), correct to four decimal places.

(c) You should find that H0 is positive and H1 is negative, what does this mean?

(d) Check your solution for P(0) by calculating the risk neutral probabilities and using the general pricing formula.