Consider contracts on natural gas maturing in 2 months with strike price $3/MMbtu. The call price is 0.3245 and the put price is 0.2625. The current futures price of a contract maturing in 2 months is 3.062.

a) What is the implied risk-free interest rate to avoid arbitrage? Hint: c₀ - p₀ = PV[S_T] - PV[X] = (PV[S_T] - PV[F₀]) + (PV[F₀] - PV[X]).

b) Suppose the risk-free rate is 3% per year. Describe an arbitrage opportunity.

c) Suppose that the next day the futures price closes at 2.987 and the call price closes at 0.3090. What must the put price close at to avoid arbitrage (assuming a risk-free rate of 3% per year).