Question

A European put option has an exercise price of £100. It has one year to expiration. The underlying stock does not pay any dividends and has a current price of £90. This price has a 50% chance of increasing to £110 and a 50% chance of decreasing to £70. The risk free rate of interest is 1% p.a. Calculate the price of the put option using the two state stock price model applying the replicating portfolio method.

Answer 1

Sol:

Stock current Price = £90

Strike price = £100

Expected to increase over one period = £110 (50% probability)

Expected to decrease over one period = £70 (50% probability)

Risk free rate = 1% p.a

CMP as on expiry can be:-

£110 or £70

Therefore, probability of both options is:-

p1 = 50% or 0.50

p2 = 1 - 50% = 50% or 0.50

To determine current value European-style put option is as follows,

Put Option premium if stock price increase to 110 = 0

Put Option premium for strike 100 = 100 - 70 = 30

Therefore, value of put option = (30 x 0.50) / (1+0.01)

Therefore, value of put option = 15 / 1.01 = £14.85

Therefore price of European-style Put option will be £14.85