I'm writing a program in R that simulates bank losses on car loans. Here is the questions I'm trying to solve:
You run a bank that has a history of identifying potential homeowners that can be trusted to make payments. In fact, historically, in a given year, only 2% of your customers default. You want to use stochastic models to get an idea of what interest rates you should charge to guarantee a profit this upcoming year.
A. Your bank gives out 1,000 loans this year. Create a sampling model and use the function sample() to simulate the number of foreclosure in a year with the information that 2% of customers default. Also suppose your bank loses $120,000 on each foreclosure. Run the simulation for one year and report your loss.
B. Note that the loss you will incur is a random variable. Use Monte Carlo simulation to estimate the distribution of this random variable. Use summaries and visualization to describe your potential losses to your board of trustees.
C. The 1,000 loans you gave out were for 180,000. The way your bank can give out loans and not lose money is by charging an interest rate. If you charge an interest rate of, say, 2% you would earn 3,600 for each loan that doesn't foreclose. At what percentage should you set the interest rate so that your expected profit totals 100,000. Hint: Create a sampling model with expected value 100 so that when multiplied by the 1,000 loans you get an expectation of 100,000. Corroborate your answer with a Monte Carlo simulation.
I'm confused about how to set up this simulation up from a high level point of view and have the following questions: 1. For part A, Should I create a pool of 1000 customers or should I create a larger pool of customers? 2. For part A, when sampling, do I sample with or without replacement? 3. For part B, I'm confused about how to set up the monte carlo simulation. Am I varying the size of the customer pool? 4. For part C, I'm not sure how to set up a sampling model that involves the interest rate. Any advice or guidance would be appreciated. I'm also thinking that if I fully understood the high level concepts for parts A and B, part C might not be such a mystery.