Contingent Claims Assignment

Suppose that we can describe the world using two states and that two assets are available, asset K
an asset L. We assume the asset’s future prices have the following distribution
State

Future Price Asset K
Future Price Asset L
$55
$45
$60
$30
The current price of asset K is $50, and the current price of asset L is $50.
1. What are the values of the unit claims (C) and C₂)?
2. What is the risk free rate implied by these assets?
3. What is the “risk neutral probability” of state 1? What is the “risk neutral probability” of
state 2?
4. What is the price implied for an asset providing $100 in state 1 and $50 in state 2?
5. You plan to buy a home for $100,000 in the future.
You want to guarantee that you will have the money.
What would you buy/sell today to accomplish this, and what would it cost today?