Question

9. Put-call parity and the value of a put option Aa Aa E Consider two portfolios A and B. At the expiration date, t, both portfolios have identical payoffs. Portfolio A consists of a put option and one share of stock. Portfolio B has a call option (with the same strike price and expiration date as the put option) and cash in the amount equal to the present value (PV) of the strike price discounted at the continuously compounded risk-free rate, which is Xem P. At expiration, the stock price is P, and the value of this cash will equal the strike price, X. Complete the equation for the put-call parity relationship: Now consider the stock of Lumia Enterprises (LE) traded at the price P = $35 per share. A put option written on LE's stock has an exercise price of X = $25 and 6 months remaining until expiration. The risk-free rate is re = 6%. A call option written on LE has the same exercise price and expiration date as the put option. If the call option has a price of Vc = $12.05, then the price of the put option is (Note: Use 2.7183 as the approximate value of e.)

Answer 1

As per the put-call parity equation, P + S = C + (K/e^rt)

where C = price of call option,

P = price of put option,

S = current stock price

K = strike price of option

r = risk free rate

t = time to expiration in years

We plug in the values to find the price of the call option :

P + S = C + (K/e^rt)

P + 35 = 12.05 + (25 / e^0.06*(6/12))

P = 12.05 + (25 / e^0.06*(6/12)) - 35

P = $1.31

The price of put option is $1.31