Suppose you are given quotes on put options on interest rates of different strikes for a given maturity (i.e. payoffs are max( K – R_T,0). For the 1% strike, the price is 0.002 and for the 2% strike, the price is 0.003. Can you construct an arbitrage based on put options of these 2 strikes? (Assume interest rates cannot go below zero.) Suppose rates can go below zero, how far below zero must rates be able to reach for an arbitrage not to exist?