UPDATED: Nov 12, 2012
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The short answer is “no.” But there is a lot more to it.
Insurance rates are determined by long term trends in actual losses and anticipated losses. When insurance premiums are being determined, current events are calculated, but they represent a small part of the equation.
In addition to insurance rates being determined over long periods of time, everything is regulated at the state level. That means what happens in one state, stays in that state. The impact of Sandy will probably be felt slightly in the states where the most damage was done, but the entire US will not feel that same impact.
One way that the cost could be impacted in other states is if reinsurers begin to increase costs to cover the impacted states. Reinsurance is basically when a separate company takes some of the risk from an insurance company in exchange for part of the premiums. If Allstate, for example, has a large exposure to risk in Florida, a reinsurer may take some of that risk while Allstate pays them. If there was a large loss in Florida, Allstate would be responsible for paying some of the payouts and the reinsurance company would be responsible as well.
Another thing that could happen is insurance companies could increase underwriting guidelines and raise rates in order to “tighten their belts.” After large events where companies must pay out large amounts of claims, insurance companies often tighten up everything in order to limit their risk exposure. After a large claim payout like Sandy, they can find themselves cash strapped and want to avoid paying out a lot more claims.
Inversely, when insurance companies find themselves with a lot of cash, they often reduce rates as a method for getting more customers. Other firms must follow suit, so you can see a general trend in reduced rates all across the board.