Hi ActEd, When calculating the URR why do we inflate/depreciate for 2.5 years? This seems to be from the average inception of the policy (halfway through the first year) to the end of the URR period (the end of the third year). Why do we not inflate/deflate to the mid point of the URR period? I.e the middle of the third year, so the adjustment is for 2 years. Many thanks, Michael
I think I can see where I was going wrong. To calculate the premium, we take the value of the car A, multiply this by the probably of writing the car off and adjust for inflation/depreciation. If a car crashes during the first year, the accident will happen on average half way through the year, so 0.5 years adjustment. Similarly for crashing in years 2 and 3, 1.5 and 2.5 years adjustment. Therefore, the URR adjustment is 2.5 years as we inflate/depreciate from the start of the first year rather than the middle of the first year. Is my understanding now correct? I think I was getting confused with applying an adjustment to a policy that incepted half way through the first year, rather than an accident that occurred half way through. This question is hard! Many thanks, Michael
Yes that's right - we are just looking at one policy and we are told in the question to assume that the car is written off mid year in each case. Therefore 2 years after inception (for a 3 year contract) there is only one more time that the car can be written off, ie in the middle of the third policy year, in other words 2.5 years after the original policy inception.
Thanks Darren. For the depreciation calculation I found myself wanting to calculate it as a compounding factor instead of subtracting the depreciation. For example, A * p * (1 + inflation %) * (1 - depreciation %). Is this a valid approach?
Not really I am afraid. You have applied the depreciation to the inflated value of the vehicle. In reality once the car is purchased its value only ever depreciates, whilst the cost of new vehicles continues to rise with inflation.
