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You need an agreed value where a particular item might be difficult to value based on what's available in the market at the time.
I imagine it's just as prevalent with watches as classic and retro cars. With cars, there might be a sliding scale of £50k in value from the lowest quality and highest quality of that particular model/trim out there, and only 2 for sale at the time when you need to make a claim, and if there's no prior documentation of the condition of your particular vehicle when you took the policy then it's very hard for you to prove that yours is on particular spot on the scale. There isn't a hard and fast value.
Surely you pay the premium for whatever the market value is at the time the time the policy is taken out. Doesn't matter whether it is a watch, classic car, fine wine or whatever. If the mug paid £20k then that's what he should be insuring it for.