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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.

  1. What is the risk free rate prevailing in the economy?
  2. 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

  1. 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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