Put-call parity states that for European call (C) and put (P) options on the same Stock Index (S), with the same exercise price (K), and time to maturity, T years then if there is a continuous dividend yield, d, then:

P₀ + S₀e^-dT = C₀ + Ke^-rT

Based on this formula determine:

a)The lower bound for European Put option prices

b)The lower bound for European Call option price

c)Determine the range of stock prices, S₀, that would ensure that the American call is not exercised early?