Assignment Task: Please use R code to answer this question:
A life insurance company is pricing a new policy to sell to a group of 45-year-old male non-smokers. They determine that the probability that a member of this group will die X years from the day they purchase the policy can be modeled with a Weibull distribution with shape parameter 4.5 and scale parameter 39, measured in years. The term of the policy is 20 years. At the end of every month, policy holders are expected to pay $115. If a policy holder in good standing dies during the term of the policy, his beneficiaries receive a lump sum of $1,000,000 at the end of the month. Every month there is a 0.3% chance that the policy holder will let the policy lapse (i.e. he will permanently stop paying premiums and forfeit his right to the benefit). The insurance company calculates cost of funds using a rate of 6.5%.
Use Monte Carlo simulation with 10,000 trials of the above scenario to calculate the net present value of cash flows to the insurance company for one policyholder.
1. Use histogram describing the NPV. How would you characterize the distribution?
2. What are the mean and standard deviation of the NPV? On balance, is the insurance company making a profit?
3. Provide a 95% confidence interval for the mean of the NPV. Interpret the result.
4. How many iterations would be necessary to provide a 99% confidence interval with a half width of $200?
5. The company can be 90% sure their npv will be at least x. Solve for x.
The company can be 99% sure their npv will be at least y. Solve for y.
Now assume the insurance company underwrites 1,000 policyholders. Use a Monte Carlo simulation with 1,000 trials to calculate the net present value of cashflows for the insurance company made to all the policy holders. (Hint: Recycle your work above. Use a list of data frames, where each element of the list represents one trial.) Answer questions (a)-(e) above under this assumption.