Here is the following extension of the three date Diamond-Dybvig model: agents can invest in following three possible technologies
–a short-term investment at date 0, that yields a return r1 =1 at date 1.
–a long term investment at date 0, that yields a return R > 1 as of date 2 but can also be liquidated at date 1 for a return L
–a short-term investment at date 1, that yields a return r2 at date 2. However, r2 is observed only at date 1.
It is assumed that :1
Note the consumption profile (C1;C2) will depend on r2; as depending on r2 agents may choose to invest in the short-term investment in date 1.
a.Describe and discuss how consumption planning C1 and C2 may change in comparison with the standard Diamond-Dybvig model without the short-investment available at date 1. (20 points)
b.The short-term investment opportunity with r2; means that the agents are exposed to interest rate risk. Discuss, why, if r2 is low, the agents will not invest in date 1 in the short-term investment, and will not be exposed to any interest rate risk. (20 points)
c. Now assume that all the agents deposit their endowments to form a bank. The bank has the same three investment technologies described above. Discuss if the exposure to interest rate risk of r2 increases or decreases the stability of the bank. (20 points)
Document Preview:
2. Here is the following extension of the three date Diamond-Dybvig model: agents can invest in following three possible technologies – a short-term investment at date 0, that yields a return r1 =1 at date 1. – a long term investment at date 0, that yields a return R > 1 as of date 2 but can also be liquidated at date 1 for a return L <>