A stock price is described in this binomial tree.

T = 0 |
T = 1 |
T = 2 |

$135 |
||

$118 |
||

$107 |
||

$100 |
||

$101 |
||

$87 |
||

$79 |

a. The sukuk risk-free rate is 7.8 percent. Compute the martingale probabilities and today’s state prices of Arrow-Debreu securities for each of the four states in year two.

b. A call option with a strike at $97 and maturing at end-year 2 is written. Compute the payoffs of the call. Compute the price of the call.

c. A put option with a strike of $102 and maturing at end-year 2 is written. Compute the payoffs of the put. Compute the price of the put.