In a one-period financial market the following securities are available for trade, the risk-free asset, yielding r= 8%; a risky security, , with time zero price (0)= 9.0740 and payoff at time given by: (1)()= 12, (1)()= 8, (1)()= 10. We introduce a put option on with strike price and maturity T=1. We denote this put option by in the sequel.

1. State whether the put option is redundant or not. Does the put option complete the market.

2. Find the interval of prices consistent with NA in the extended market. If the put has time zero price 1.75925 are there arbitrage opportunities?

3. Under the same assumptions of point 2, state whether the extended market gives rise to violations of the Law of One Price.

4. State whether the payoff :

(1)()= 0

(1)()= 0

(1)()= 10

is redundant in the extended market and, if that is the case, find the replication cost of the security. Does the introduction of in the market generate violations of the Law of One Price? Does it generate arbitrage opportunities?

K = 11 K = 11