(m) An investor has purchased the bottom tranche of a mortgage-backed security (MBS) con- sisting of 10 similar mortgages. This is the tranche that is first affected when one of the mortgages that make up the MBS defaults, and thus the investor is particularly interested in the first time T that one of the mortgages defaults. As a simplifying assumption, the investor assumes that the default times 71, ..., 710 of the mortgages that make up the MBS are independent exponentially distributed with parameter A. Then the first-to-default time is T = min{71,..., 710}. By looking at historical data, the investor notes that five MBS with identical structure and characteristics had first-to-default times T₁ = 1.2, T2=0.9, T3 = 2.1, T₁ = 1.5, T5 = 1.3. What is the maximum likelihood estimate estimate of X? Round your answer to 3 decimal places. [Hint: First compute the PDF of T.]
(m) An investor has purchased the bottom tranche of a mortgage-backed security (MBS) con- sisting of 10 similar mortgages. This is the tranche that is first affected when one of the mortgages that make up the MBS defaults, and thus the investor is particularly interested in the first time T that one of the mortgages defaults. As a simplifying assumption, the investor assumes that the default times 71, ..., 710 of the mortgages that make up the MBS are independent exponentially distributed with parameter A. Then the first-to-default time is T = min{71,..., 710}. By looking at historical data, the investor notes that five MBS with identical structure and characteristics had first-to-default times T₁ = 1.2, T2=0.9, T3 = 2.1, T₁ = 1.5, T5 = 1.3. What is the maximum likelihood estimate estimate of X? Round your answer to 3 decimal places. [Hint: First compute the PDF of T.]
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
![(m) An investor has purchased the bottom tranche of a mortgage-backed security (MBS) con-
sisting of 10 similar mortgages. This is the tranche that is first affected when one of the
mortgages that make up the MBS defaults, and thus the investor is particularly interested
in the first time T that one of the mortgages defaults.
As a simplifying assumption, the investor assumes that the default times 71, ..., 710 of the
mortgages that make up the MBS are independent exponentially distributed with parameter
A. Then the first-to-default time is T = min{71,..., 710}.
By looking at historical data, the investor notes that five MBS with identical structure and
characteristics had first-to-default times
T₁ = 1.2, T2=0.9, T3 = 2.1, T₁ = 1.5, T5 = 1.3.
What is the maximum likelihood estimate estimate of X? Round your answer to 3 decimal
places.
[Hint: First compute the PDF of T.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34c4e224-21c9-4843-bd53-78f228ae29a9%2F4ab33790-e636-4280-9b65-7dd9001180c3%2F6ufsbc7_processed.png&w=3840&q=75)
Transcribed Image Text:(m) An investor has purchased the bottom tranche of a mortgage-backed security (MBS) con-
sisting of 10 similar mortgages. This is the tranche that is first affected when one of the
mortgages that make up the MBS defaults, and thus the investor is particularly interested
in the first time T that one of the mortgages defaults.
As a simplifying assumption, the investor assumes that the default times 71, ..., 710 of the
mortgages that make up the MBS are independent exponentially distributed with parameter
A. Then the first-to-default time is T = min{71,..., 710}.
By looking at historical data, the investor notes that five MBS with identical structure and
characteristics had first-to-default times
T₁ = 1.2, T2=0.9, T3 = 2.1, T₁ = 1.5, T5 = 1.3.
What is the maximum likelihood estimate estimate of X? Round your answer to 3 decimal
places.
[Hint: First compute the PDF of T.]
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