Question

Consider a European-style call option on a stock that is currently trading at £100. The strike price of the call is £90. Assume that, in the next 12 months, the stock price can either go up to £120 or go down to £80. Using risk-neutral valuation, calculate the current value of the option if the risk-free rate is 5 percent per annum. Use discrete compounding. Which of the following is correct?

A. £18
B. £18.5
C. £18.75
D. £19

Answer 1

Sol:

Stock current Price = £100

Strike price = £90

Expected to increase over next period = £120

Expected to decrease over next period = £80

Risk free rate = 5%

CMP as on expiry can be:-

£120 or £80

Therefore, probability of both options are:-

p1= {CMP(1+r)-S2}/(S1-S2)  

where,

CMP = Current CMP

S1 = High CMP as on expiry

S2 = Low CMP as on expiry

p1 = 100(1+0.05) - 80}/(120 - 80)

p1 = 25 - 40 = 0.625

p2 = 1 - 0.625 = 0.375

1) Current value European-style call option,

Call Option premium for 120 = 120 - 90 = 30

Call Option premium for 90 = 0

Therefore, value of call option = (30 x 0.625) = £18.75

Therefore current value European-style call option will be £18.75

Ans is C - £18.75