Financial Crisis Coursework

Financial Crisis Coursework 2

Problem1.

Under no arbitrage condition=1[pic 1]

[pic 2]

[pic 3]

For (a)

[pic 4]

[pic 5]

       [pic 6][pic 7]

        [pic 8][pic 9]

So price vector (a) is consistent with equilibrium

For (b)

[pic 10]

     [pic 11][pic 12]

       [pic 13][pic 14]

[pic 15]

So price vector (b) is not consistent with equilibrium

For (c)

[pic 16]

[pic 17]

     [pic 18][pic 19]

       [pic 20][pic 21]

So Price vector (c) is not consistent with equilibrium

Problem 2

[pic 22]

[pic 23]

[pic 24]

So the quantities satisfy the consumer’s budget constraint

At date 1, after the true states has been revealed consumers can buy goods for delivery at dates1 and 2 subject to budget constraint

[pic 25]

So     [pic 26][pic 27]

       [pic 28]

       [pic 29][pic 30]

       [pic 31]

If     [pic 32][pic 33]

So at date 0=1[pic 34]

So satisfy     the budget constraint[pic 35]

Problem 3

As we treat consumption at date 1 as numeraire in each state  [pic 36][pic 37]

[pic 38]

[pic 39]

The price in date 2 should be adjusted

[pic 40]

[pic 41]

Consumption of Arrow securities

[pic 42]

[pic 43]

The budget constraint is          [pic 44]

So [pic 45]

As =1 remain the same[pic 46]

[pic 47]

So the price of Arrow security [pic 48]

Problem 4

                            Region A        Region B

State (H, L)                                      [pic 49][pic 50]

State (L, H)                                       [pic 51][pic 52]

[pic 53]