Question

1.              Metropolitan Builders’ common stock is currently selling at $60. You estimated that it has a standard deviation of 0.35. Assume the risk-free interest rate is 3 percent per year.

a)What is the maximum you would pay for a 26-week put option with an exercise price of $65 on Metropolitan Builders’ stock?

b)If you can’t sell a share short, you can achieve exactly the same final payoff by a combination of risk free bonds and options. What is the combination? Please describe in words.

Answer 1

Using the Black scholes model we would calculate the price of put option,

P = Ke^(-r*T)*N(-d2) - S*N(-d1)
P= 65e(-0.03^0.50)*N(-d2) - 60*N(-d1)
d1= (ln(S/K) + (r + (annualized volatility)^2 / 2)*T) / (annualized volatility * (T^(0.5)))
d2 = d1 - (annualized volatility)*(T^(0.5))
d1 =(In(60/65) +(0.03 + (35^2)/2)*0.50)/(35*(0.50^0.50))
Solving above we get d1 = -0.13907
d2 = -0.13907 -((35)*(0.50^0.50))
solving above we get d2 = -0.38656
Using the normal distribution table
N(-0.13907) = 0.44470
N(-0.38656) = 0.34954
P= 65e(-0.03^0.50)*0.34954 - 60*0.44470
Solving above we get price of put option = $8.33215

b) If you can't sell a share short, you can achieve exactly the same final payoff by a combination of risk free bonds and options. This combination is known as replication of portfolio options. This strategy is used by the investors to hedge the risk due to loss in options by taking opposite position in risk free bonds that is investing an equal amount to earn no loss and no profit scenario. In this the exact amount which is invested either in purchase of option same is invested in risk free asset to hedge the loss from options. In this portfolio one is the risky asset and the other is the riskless asset.