How maths killed Lehman Brothers
You can in fact calculate it, easily. The 100 customers each have a 3% chance of defaulting, so you expect three customers to default next year. That is, you will need to pay $3 million next year. Assuming the interest rate is about 3% each year, next year's $3 million would be worth 3/(3/100+1)=3/1.03=2.91 million now. Therefore HSBC will have to pay you at least $2.91 million for the insurance. Obviously Lehman Brothers wasn't a charity and so, to make money, they would double the price to $5.82 million and expect to make $2.91 million out of each of these deals on average. This kind of insurance is called a credit derivative swap (CDS).