Question

The common stock of the P.U.T.T. Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next 3 months. You do not know whether it will go up or down, however. The current price of the stock is $160 per share, and the price of a 3-month call option at an exercise price of $160 is $6.73.

a. If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on P.U.T.T. stock at an exercise price of $160? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. A straddle would be a simple options strategy to exploit your conviction about the stock price’s future movements. How far would it have to move in either direction for you to make a profit on your initial investment? (Round your intermediate calculations and final answer to 2 decimal places.)

Answer 1

a)Here we can use the Put-call parity equation since both options are on the same underlying asset and also the strike price/exercise price & Maturity period are the same.

Vc+Present value of strike price=Vp+Vs

Vc=Value of share=6.73

Vp=Value of put=?

Vs=Value of share=160

Present value of strike price=Step 1

Step 1 Present value of strike price

PV =160*e^-rf*t

rf=10%

t=3/12

Apply equation=e^0.10*3/12

e^-0.025=1/1.02531=0.9753

160*0.9753=156.05

Value of Put

6.73+156.05=Vp+160

162.78-160=Vp

2.78=Vp

Answer b)

Straddle long

Breakeven FSP=

Upper=160+2.78+6.73=169.51

Lower=160-2.78-6.73=150.49

If fsp >169.51 Profit due to call option

If fsp<150.49 profit due to put option