According to the insurance website InsuranceNEWS.com.au (selective quotes):
Money has triumphed over fear in the New Zealand reinsurance market. Higher reinsurance rates are attracting reinsurers who have not normally operated in the market, offsetting fears that capacity is shrinking.
.. reinsurers from Bermuda and Europe as well as Lloyd’s have entered the New Zealand market as a result of higher rates.
But with reinsurance rates for New Zealand increasing up to 500% at the July renewals, Mr De Souza says Aon has been able to find takers for all the business it wants to place.
... while the largest insurers – such as the Australian companies which dominate the New Zealand insurance market – will continue to get reinsurance cover (“they are just going to have to pay more”), smaller companies might find the cost of operating in New Zealand is prohibitive and not worth their while.
For a lot more information, and the quotes in context, see the analysis report here.