Economics 434 Financial Markets Professor Burton University of Virginia Fall 2015 September 8, 2015

Today Tomorrow s1s1 s3s3 s2s2 And, we may not have any idea what the probabilities of s 1, s 2, s 3 may be!! September 8, 2015

So, Again, What are “State Prices” A state price, q i, is the price of a security that returns $ 1 in state i The rate of return of the i th state price security would be: (1 – q i ) divided by q i September 8, 2015

Fundamental Theorem of Finance The Assumption of No Arbitrage is True If and only if There exist positive state prices (one for each state) that represent the price of a security has a return of one dollar in that state and zero for all other states September 8, 2015

How can you use “state prices?” To price any security – Price of a security j equals: P j = (p j,1 * q 1 ) + (p j,2 * q 2 ) + (p j,3 * q 3 ) This pricing formula is true if and only if the no- arbitrage assumptions is true September 8, 2015

The Risk Free Security September 8, 2015

Interpreting the risk free rate September 8, 2015

Create pseudo-probabilities (risk adjusted probabilities) September 8, 2015

Again: How can you use “state prices?” To price any security – Price of a security j equals: P j = (p j,1 * q 1 ) + (p j,2 * q 2 ) + (p j,3 * q 3 ) This pricing formula is true if and only if the no- arbitrage assumptions is true September 8, 2015

The Pricing of Security j September 8, 2015