Ward said the London market had put in place a contingency plan to switch euro underwriting to multi-currency settlement if Greece abandoned the euro.
Greece has implemented austerity measures in return for two multi billion euro bailouts, however after five years of recession and new elections in the country in June, pro-austerity politicians have become increasingly unpopular.
If the leftist bloc Syriza comes into power it may abandon austerity measures and be forced out of the euro.
This could trigger a run on banks not only in Greece but in other eurozone nations.
Lloyd’s of London is an insurance and reinsurance market where syndicates meet brokers and agree to take on particular risks. Not to be confused with the financial institution Lloyds Banking Group.
Ward said: “We’ve got multi-currency functionality and we would switch to multi-currency settlement if the Greeks abandoned the euro and started using the drachma again.
“I don’t think that if Greece exited the euro it would lead to the collapse of the eurozone but what we need to do is prepare for that eventuality.”