3. In each month, the nondividend-paying stock of Chiron, a drug company, can either appreciate or depreciate by x% in value with probability 0.3 or 0.7 , respectively. The initial price of the stock is $30 per share and the risk-free rate is 0.5% per month. (a) What are the prices of at-the-money European call options on this stock, which expire two months from now with x=1,5,10, and 15 , respectively? 1 (b) Plot the call option prices calculated in part (a) against the volatility, x. (c) Repeat parts (a) and (b) for at-the-money European put options on this stock that expire two months from now with x=1,5,10 and 15 , respectively? (d) What do you find from the graphs in parts (b) and (c)? Explain why the observed relationships prevail