Consider a three-period binomial tree model for a stock price process Stunder which the stock price either rises by 18% or falls by 15% each month. No dividends are payable. The continuously compounded risk-free rate is 0.25% per month. Let S0 = $85. Consider a European put option on this stock, with maturity in three months (i.e. at time t = 3) and strike price $90.

1. (a) State the conditions under which the market is arbitrage free.

2. (b) Verify that there is no arbitrage in the given market.