State Prices and Market Completeness

Question 1

In a complete market, every contingent claim can be replicated by a portfolio of traded assets.

Answer 1

Answer: True
→ Market completeness means any payoff can be constructed using existing assets.

Question 2

In an incomplete market, state prices do not exist.

Answer 2

Answer: False
→ State prices can still exist, but they may not be unique.
→ Completeness guarantees unique state prices.

Question 3

The existence of at least one positive set of state prices ensures the market is complete.

Answer 3

Answer: False
→ Existence of positive state prices ensures no arbitrage, not completeness.
→ Uniqueness of state prices characterizes completeness.

Question 4

If the number of traded assets equals the number of states of nature, the market is always complete.

Answer 4

Answer: False
→ Only true if the payoff matrix is invertible (full rank).
→ Assets could be redundant (linearly dependent).

Question 5

State prices can be interpreted as the present value of a one-unit payoff in a specific state of the world.

Answer 5

Answer: True
→ That’s precisely the definition of an Arrow-Debreu state price.