Calculating the premium rate

When times were less civilized, people used to pay fortune-tellers to predict the future. Will a tall, dark stranger come into your life next week? Will you win more than you lose in life’s game? Although the modern actuaries may not be quite so good on the hair color of the people you will meet next week, they are very good at estimating a whole range of things about your life. As a driver, they can estimate the risk you will have an accident during the next year. As a home owner, they can predict the probability you will suffer a burglary. Depending on your health record, they can suggest the diseases and disorders you are most likely to catch. They are experts on life expectancy. So, when it comes to setting the premium rates for whatever policy you are proposing to buy, they have already placed you in a group. At this point, we need to refer to the National Health and Nutrition Examination Survey which, among other things connected with the health of the nation, monitors body weight. The results of the most recent survey show that almost two-thirds of all Americans are overweight and about one-third are considered clinically obese. Should the present rate of increase be maintained, the entire population should be considered obese come 2050. Except, of course, there will always be some who insist on being thin. Why should this matter? Because obesity has a direct bearing on life expectancy. The heavier you are, the shorter your expected span of years. Worse, as the weight rises, so do the chances of long-term illnesses so, even if you do continue life, it may well involve long-term nursing care. Not surprisingly, one of the standard questions to resolve while the insurers decide whether to issue a policy and, if so, at what premium rate, is your weight. Although simply carrying an extra few pounds is not a pre-existing medical condition, the moment you admit an above-average body mass index for your age, the medical exam will become more thorough. There will be particular interest in the level of cholesterol and other lipids in your bloodstream, and then tests over time to discover whether your blood pressure is rising, whether your arteries are hardening and whether the first signs of heart disease are present. The more serious any symptoms, the less likely it is the insurer will agree to insure you, or the insurer will only offer a policy with a higher than expected premium rate. Is this fair? Well it all depends on whose point of view you take. You want to provide financial security for your family. The life insurance company wants to make a profit and stay in business. The issue to resolve is therefore simple. If the insurer only expects you to live another twenty years, the premium you pay must cover the expected benefits. The premium rate will fall if the company believes you will live a further forty years. Now it comes back to you. If you want a reasonable life insurance rate, you can lose weight, begin a program of exercise and improve your health. In life, you earn rewards in many different ways. In this case, lower rates come through dieting.

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Given a 2.0 year spot and a 1.5 year spot, we want to solve for the six month forward staring in 1.5 years. That’s the forward rate denoted by 1f3 or 0.5f1.5.
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