Use no-arbitrage arguments to prove the following claims. That is, for each claim, provide the usual step-by-step proof by contradiction: assume that the claim does not hold, guess an arbitrage trading strategy, and verify that the trading strategy is indeed an arbitrage by showing that the payoffs are never negative and sometimes strictly positive.

(a) The premium (or price) of a call is a decreasing function of the exercise price.

(b) The premium (or price) of a put is an increasing function of the exercise price.

(c) The value of a put is greater than XerT S0.

(d) The value of a derivatives that gives you the obligation to buy the stock at price

X at time T is S0 XerT .