Question

1- A one-year European call option on Stanley Industries stock with a strike price of $55 is currently trading for $75 per share. The stock pays no dividends. A one-year European put option on the stock with a strike price of $55 is currently trading for $100. If the risk-free interest rate is 10 percent per year, then what is the current price on one share of Stanley stock assuming no arbitrage?

2- The current price of MB Industries stock is $20 per share. In the next year the stock price will either go up to $24 per share or go down to $16 per share. MB pays no dividends. The one year risk-free rate is 5 percent and will remain constant. Using the one-step binomial pricing model, what is the price of a one-year CALL option on MB stock with a strike price of $20 (out to two decimal places)?

3- The current price of MB Industries stock is $20 per share. In the next year the stock price will either go up to $24 per share or go down to $16 per share. MB pays no dividends. The one year risk-free rate is 5 percent and will remain constant. Using the one-step binomial pricing model, what is the price of a one-year CALL option on MB stock with a strike price of $20 (out to two decimal places)?

4- A European call and a European put on the same stock have the exact same strike price and the exact same expiration. At 10:00am on a certain day, the call option premium is $3.25 and the put option premium is $4.25. At 10:01am news reaches the market that no effect on the stock price or on interest rates, but it does increase volatilities. As a result, the call premium increases to $4.00. What is the new put premium (out to two decimal places)?

Answer 1

From the put call parity equation

c+ K/(1+r)^t = p+S

where c and p are call and put option premiums respectively

K is the strike price of the options

, r is the periodic interest rate

and t is the no. of periods

, S is the spot price of stock

For no arbitrage, the put-call parity must hold

S = 75+55/1.1-100 =$25

No arbitrage price of Stanley's stock is $25

(It may be noted that European Put option cannot trade above present value of strike price ie. $50, Also European call option cannot trade above current stock price i,e, $25)