economics, Mathematics

Assignment Help:
A mortgage lender seeks to maximize the expected value of its portfolio. The portfolio, of course, is the
sum of all of the mortgages in it, so no generality is lost by examining the case of one loan:
E[port] = (1-p).B +p.(V-L)
where:
_ E[port] is the expected value of the portfolio
_ p is the probability of foreclosure
_ B is the principal balance
_ V is the sale price at foreclosure
_ L is the legal fees incurred by foreclosure
Assume that the borrower’s probability of foreclosure is an increasing function of his/her ”balance-to value ratio” (i.e. B/V):
P ? p (B/V) P’>0
In other words, borrowers who are deeper underwater are more likely to enter the foreclosure process. In such cases, reducing principal balances would reduce foreclosure-related losses (by reducing the probability of foreclosure). On the other hand, principal balance reductions are a direct loss for the lender.
1. Derive the marginal benefit of reducing principal balances.
2. Derive the marginal cost of reducing principal balances.
3. What is the necessary condition for maximizing E[port] with respect to the principal balance?
4. What is the sufficient condition for maximizing E[port]?
5. How does the marginal benefit curve shift in response to an increase in L?
6. How does the marginal cost curve shift in response to an increase in L?
7. How does the optimal principal balance change when L increases?

Related Discussions:- economics

Write triangles named by the lengths of their sides, Write Triangles Named ...

Write Triangles Named by the Lengths of Their Sides? An equilateral triangle is a triangle with three congruent sides. All three sides of this triangle are the same lengt

How to left shifts and right shifts a graph, Q. How to Left shifts and righ...

Q. How to Left shifts and right shifts a graph? Ans. When you're translating (shifting) a graph, it's easy to get subtracting and adding mixed up. It seems counter-intuiti

Greatest common factor, x 4 - 25 There is no greatest common factor her...

x 4 - 25 There is no greatest common factor here.  Though, notice that it is the difference of two perfect squares. x 4 - 25 = ( x 2 ) 2   - (5) 2 Thus, we can employ

Explain adding negative fraction, Explain Adding Negative Fraction? To...

Explain Adding Negative Fraction? To add negative fractions: 1. Find a common denominator. 2. Change the fractions to their equivalents, so that they have common denominators

GEOMETRIC PROGRESSION, THE FIRST AND THIRD TERM OF A G.P ARE 8 AND 18 RESPE...

THE FIRST AND THIRD TERM OF A G.P ARE 8 AND 18 RESPECTIVELY AND THE COMMON RATIO IS POSITIVE.FIND THE COMMON RATIO

Arithmetic sequence, find a30 given that the first few terms of an arithmet...

find a30 given that the first few terms of an arithmetic sequence are given by 6,12,18...

Example of repeated eigenvalues, Illustration : Solve the following IVP. ...

Illustration : Solve the following IVP. Solution: First get the eigenvalues for the system. = l 2 - 10 l+ 25 = (l- 5) 2 l 1,2 = 5 Therefore, we got a

Fraction, One day it snowed 3 and 3/8 inches in Altoona and 3.45 inches in ...

One day it snowed 3 and 3/8 inches in Altoona and 3.45 inches in Bethlehem. Which city received less snow that day.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd