Question

1. Consider a stock with price S = $100 at t = 0. The interest rate is 10% compounded continuously. (a) [10pts] Determine the upper and lower bounds on the price of a European call option at t = 0 with strike price $120 and expiration T = 1 year. (b) [10pts) If the price of a European call with strike price $120 and expiration T = 1 year at t = 0 is $50, use put-call parity to determine the price of a European put option with the same strike price and expiration date.

Answer 1

Solution:

Spot Price = 100 , Strike Price (X) = 120, T = 1 ,r = 10%

A) The value of the call option is Max(S-X,0) i.e. the lower bound is 0 and upper bound is S-X.

In our case lower bound = 0 , Upper bound = Spot Price - Strike Price (100 -120) {Cant be negative , So the call is valued at 0}

B) We know as per the put call parity theorem:

P + S = C + X*e^(-rt)

P => Price of the put, S=>Spot price , X =>Strike Price, r =>rate , t => time to maturity , C => Call price

We have been given ,

P =? , C = 50 , S =100 , X =120 , t =1 , r = 10% or .1

Putting the values we get

P + 100 = 50 + 120* (e^(-.1*1))

P +100 = 50 + 120*.9048

P = 50 + 108.5804 -100 = 58.5804

The Price of the put option comes out to be $58.5804