In finance, one example of a derivative is a financial asset whose value is determined (derived) from a bundle of various assets, such as mortgages. Suppose a randomly selected mortgagein a certain bundle has a probability of 0.06 of default.(a) What is the probability that a randomly selected mortgage will not default?(b) What is the probability that four randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the others? Note: A derivativemight be an investment that only pays when all four mortgages do not default.(c) What is the probability that the derivative from part (b) becomes worthless? That is, at least one of the mortgages defaults.(a) The probability is(Type an integer or a decimal. Do not round.)

We are given that the probability of a mortgage to be default is 0.06 (say p)

Answered: In finance, one example of a derivative…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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7. An investment analyst has tracked a certain blue-chip stock for the past six months and found that on any given day it wither goes up a point or down a point. Furthermore, it went up on 25% of the days and down on 75%. What is the probability that at the close of trading four days from now, the price of the stock will be the same as it is today? Assume that the daily fluctuations are independent events
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Consider a whole life insurance with annual premiums and a 20-year premium paying term issued to a select life aged 30, with sum insured $200,000 payable at the end of the year of death. (a) Write down an expression for the net future loss random variable. (b) Calculate the net annual premium.
8 In a supermarket, the prices marked on the signs that are placed on the shelf do not always correspond to the current price of the merchandise, since errors may occur when recording price changes. Assume that over time 60% of the price changes are increases and 40% are decreases. Assume also that 93% of the price increases are marked correctly, as are 98% of the reductions. If a price is not marked correctly, what is the probability that the change is a reduction?.
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Suppose that we have test for lung cancer, which correctly identifies those with the cancer 70 % of the time, and mistakenly identifies those without the cancer 5 % of the time. In the cohort of interest, the rate of this cancer is somewhat low: 0.9 %. Find the probability -- a number between 0 and 1 -- that someone diagnosed (testing positive) with this test actually has lung cancer.
An antique collecter has been following the price of a certain old camera and he found out that the camera's price changes each day and it can either rise or fall in value. The price changes per day are assumed to be independent events. After observing the price for 8 months, he found out that the price rose for 40% of the days and it sunk for the rest. He wants to determine the probability that the camera will be a certain value on a particular day so he asked you for help. 1) What distribution does this problem follow? (Geometric, Binomial, Poission?) 2) Determine the probability that 7 days from now, the cost of the camera will be the same as it is today.3) Determine the probability that the camera's cost has increased from its current value after 5 days.
b. Demand for electricity next year is projected to be one of the following quantities: 18,000GWH with probability of 0.4, 25,000GWh with probability of 0.4, or 30,000GWH. i. If this year's demand is 17,500GWH, what should be the additional amount to plan against if the energy ministry would want to plan for the increase using expected value analysis? ii. What is the standard deviation of the suggested accompanying amount?
1
A mortgage holding company has found that 0.09 of its mortgage holders default on their mortgage and lose the property. Furthermore, 0.93 of those who default are late on at least two monthly payments over the life of their mortgage as compared to 0.38 of those who do not default. What is the joint probability that a mortgagee has two or more late monthly payments and does not default on the mortgage? 0.3458 0.0342 0.0837 0.8463

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