Question

Problem 5. An insurance company's losses of a particular type are to a reasonable approximation normally distributed with a mean of $150 million and a standard deviation of $50 million. (Assume no difference between losses in a risk-neutral world and losses in the real world.) The 1-year risk- free rate is 5%. Estimate the cost of the following: (a) A contract that will pay in 1 year's time 60% of the insurance company's losses on a pro rata basis. (b) A contract that pays $100 million in 1 year's time if losses exceed $200 million.

Answer 1

I have answered the question below

Please up vote for the same and thanks!!!

Do reach out in the comments for any queries

Answer:

Following information applies to all the parts of the question: Extracted Information Losses of the insurance company are normally distributed Mean = $150 million Standard deviation = $50 million One year risk free rate = 5% PART (A) Estimate the cost of the following contract In millions of dollars, the losses are approximately (150,50) The contract of reinsurance would reimburse out only 60% of the losses. Thus, the pay-out from the reinsurance contract is (90,30) The reinsurance cost is the pay-out expected in the world where the risk is neutral, which are discounted at the risk free rate. In this situation the pay-out expected is similar in the neutral risk world as it is there in the real world. Thus the value of reinsurance contract is 90e 0.08x1 = $85.61 million Thus, the cost of this contract is $85.61 million

PART (B) Extracted Information Contract will pay $100 million in 1 years' time if losses move ahead of $200 million. In this case the chance that the losses will be greater or higher than the $200 million is the probability that the normally distributed variable is higher than one standard deviation ahead of the mean. That is, 0.1587. The expected payoff is therefore 0.1587x100 = $15.87 million and the value of the contract is 15.87€ 0.05x1 = $15.10 million Thus, the value of this contract is $15.10 million