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Estimating Costs of Contracts

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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 one-year risk-free rate is 5%. Estimate the cost of the following:

a. A contract that will pay in one year's time 60% of the insurance company's costs on a pro rata basis.
b. A contract that pays $100 million in one year's time if losses exceed $200 million.

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This solution provides steps necessary to estimate the cost of the two contracts.

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a. A contract that will pay in one year's time 60% of the insurance company's costs on a pro rata basis.
Because the insurance company's losses are to a reasonable approximation normally ...

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