13. In a one-period setting, suppose there are three states of the world at the end of the period. Suppose there are three securities, stocks A and C, and a risk-free bond B. The initial prices of securities A, B, and C are, respectively, 20, 1, and 10. The prices after one period are as given in the table below:
| Security | State 1 | State 2 | State 3 |
| A | 50 | 20 | 5 |
| B | 1.10 | 1.10 | 1.10 |
| C | 20 | 30 | 2 |
(a) Using replication, find the price of a call option on stock A at a strike price of K = 15.
(b) Using replication, find the price of a call option on stock B at a strike price of K = 15.
(c) What are state prices? Compute these for the three states in the model. (State prices are defined in Appendix 11 B.)
(d) Show how you would price the two call options above using state prices.
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