Suppose Lotus stock price is Currently $50. A six-month European call option on

Question

Suppose Lotus stock price is Currently $50. A six-month European call option on the stock with exercise price of $48 is selling for $6. A six-month European put option on the stock with exercise price of $48 is selling for $3.50. The risk free interest rate is $15% per annum. Is there any arbitrage opportunity? If you answer yes to , please show your arbitrage strategy. Show the cash flows at t = 0 and cash flows at t = 6 months if the stock is $60 or $30 Cash Flows at t = 0 Cash Flows at t = 1 if S = 60 Cash Flows at t = 1 if S = 30

Explanation / Answer

a. Future price of stock = $50 ( 1 + 0.15 x 6/12)

= $53.75

Yes, there is a arbitrage opportunity

b. Investor should buy 1 call option by paying $6 at a strike price of $48

After six months future price = $53.75 which will enable the investor to excercise the call option

Gain on excercise of call option = (53.75 - 48)

= $5.75

  

Gain on excercise of put option

48 - 30 = 18

Cash flows at t=0 Cash flows at t=6 months, if Stock price = $60 ( Call option) Cash flows at t= 6 months , if stock price = 30 (Put option) Premium = $6 + 3.50 Gain on excercise of call option = 60 - 48 = 12

Gain on excercise of put option

48 - 30 = 18

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