No-Arbitrage

The first course video is simply one introducing the course.  For that purpose, I will skip posting about it.  I will instead continue on to the post about no-arbitrage.

For a contract, ck is cash flow at time k and p is price of a contract

Weak no-arbitrage - if ck ≥ 0 for all k ≥ 1 then p ≥ 0
Strong no-arbitrage - if ck ≥ 0 for all k ≥ 1 and cl > 0 for some l then p > 0

Basically weak no-arbitrage says that if the total payout is equal to or greater than 0, then the price is equal to or greater than 0.  Strong no-arbitrage says that if the total payout is greater than 0, then price is greater than 0.

Implicit assumptions are that markets are liquid and price information is available to all buyers and sellers (complete Arrow-Debreu markets).


An example:

This gives us a lower bound on the price of the bond: A/(1+r)

This gives us the upper bound on the price of the bond: A/(1+r)

The two results imply that p = A/(1+r)