” 辅导CFRM 542程序、R编程 写作、 辅导program程序CFRM 542 Credit Risk Management Fall 2020 Assignment 2CFRM 542 Assignment #2Due: Wednesday, October 28th at 11:59 PM Pacific timeInstructions: Complete problems 1-3 below. Document your results in a single electronic file, such as aMicrosoft Word document, and show all of your work. For problem 1 you may wish to submithandwritten results for (a)-(d), in which case you can scan and include this in the electronic document asan image. Submit your completed assignment to the drop box on the course website. You may discussthis assignment with your classmates and TA but the work you submit, including your code and resultsfrom R, must be your own.1. Maximum Likelihood Estimation. Consider a set of data with N total observations, of which Dcontain the event we are trying to model (e.g. in our Coronary Heart Disease example, N is 100and D is the number of patients with CHD).a. Write down a logistic probability function to model this data using only an interceptterm i.e., there is no independent variable.b. Write down the likelihood function and the log likelihood function based on thisintercept-only model.c. Write down the derivative of the log likelihood with respect to the unknown interceptparameter.d. The log likelihood is maximized in this example when the derivative is equal to zero. Usethis to show that the maximum likelihood probability =2. Logistic Regression Analysis 2.a. Write a function in R to calculate the K-S statistic, as defined in the lecture 4. Yourfunction should take as input two vectors. The first vector is the (not sorted) list ofprobability estimates and the second vector is the vector of corresponding actualoutcomes (i.e., a vector of 1s and 0s). Submit the R code defining your function.b. Use your function and the CHD data from class. What is the KS of the best fit logisticregression between age and CHD? Show the R commands used to calculate this.c. Using the Lending Club data from assignment 1, create and submit a plot of log odds ofdefault vs. revolving line utilization using 20 bins. What do you observe?d. Make a best fit logistic regression between default and revolving line utilization. In yourmodel, do something to account for higher default risk at the lowest utilization level andmodel the relationship between utilization and log odds of default as piecewise-linear intwo parts. Create and submit a plot of model vs. actual log-odds as a function ofutilization. Submit your script and the summary regression results from R.CFRM 542 Credit Risk Management Fall 2020 Assignment 23. Working with credit transitions. Use the credit rating transition matrix from Lecture for thisproblem.a. What is the probability distribution of credit states for a AAA credit after 3 years? Whatis the probability distribution after 5 years?b. Make a table showing the probability of default over 1, 2, 3, and 5 years for each of thestarting 7 credit grades (AAA through CCC)c. As the time horizon over which you project the credit transitions increases, what is thelimiting probability distribution for each starting credit grade? i.e., as the number ofyears increases to infinity, to what does the probability distribution of credit statesconverge? After you have figured out the limiting behavior (you may experiment toform your hypothesis) write down an argument for why this must be the case. A fewwell-written sentences explaining the dynamics and the limiting behavior will earn fullcredit. If you remember enough linear algebra, you can prove this limiting behaviormathematically.如有需要，请加QQ：99515681 或邮箱：99515681@qq.com
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