Question: Consider 3 securities: A, B and C that will generate the following payoffs to investors next year: State Security A Security B Security C Boom
Consider 3 securities: A, B and C that will generate the following payoffs to investors next year:
| State | Security A | Security B | Security C |
| Boom | $100 | $0 | $0 |
| Normal Economy | $0 | $100 | $0 |
| Recession | $0 | $0 | $100 |
The three possible states of the economy are equally likely. Security A is trading today for $20, Security B is priced at $30 today, and the price of Security C today is $40.
- What is the risk free rate prevailing in the economy?
- What is the price of securities X and Y? They have the following payoffs:
| State | Security X | Security Y |
| Boom | $50 | $100 |
| Normal Economy | $50 | $40 |
| Recession | $200 | $0 |
- Suppose, your investment banker suggests a synthetic option zeta on X and Y. The option zeta matures in one year. At maturity zeta pays the difference between X and Y, if payoff from security X is greater than the payoff from security Y. Zeta pays nothing if the payoff from security Y is greater than the payoff from security X. That is, the payoffs from zeta are : Z = max [0, X Y]. At what price would you purchase zeta today?
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