Bilco’s shares trade on the NYSE, while options on the stock are traded on the CBOE. The stock currently trades for $40 and both 3 months calls and 3 months puts on the stock are currently available with exercise price of $45. The risk-free rate is 2% per year or 0.5% for three months.
a. You estimate that the stock price can either go up by 25% or down by 25% over the next three months. Use the binomial approach to value the put option.
b. Use the Put-Call parity and the put value computed in 2.a to determine the value of the call. (If you could not compute the put price, assume the put price is $7.)
c. You observe that the Call currently trades for $3.50. If the Call is mispriced, describe the mispricing in words and describe in detail the trading strategy you can use to take advantage of the mispricing at no risk. What is the arbitrage profit for each Call bought or sold? (hint: use the Put-Call parity)
d. Draw the payoff, and profit and loss diagram of the strategy of buying a Call with exercise price of $35 while selling simultaneously a Call with exercise price of $45. Determine the break-even stock prices given that the price of the Call with exercise price of $35 is $7.5 and the price of the $45 exercise price Call is $2.50.