Question

The current futures price of a stock is $15 per share. One month later, when the futures option expires, the futures price could have risen to $16.5 per share or declined to $14 per share. The strike price is $14.5. The risk-free rate is 6%.

What is the value of long futures contract (per share) at the option maturity? (1 mark)

Answer 1

step - 1:

first we have to calculate probability of upward and downward movement

highest future price(H) = 16.50

Lowest price (L) = 14

Probabilty of highest price (upward) = (current price*e^rt - L) /( H - L)

r = risk free rate = 6%

t = time period = 1 month = (1/12)

Probabilty of highest price (upward) = 15*e^0.06*(1/12) - 14 / (16.50 - 14)

= 0.430

Probability of lower price = 1 - Probabilty of highest price

= 1 - 0.430

= 0.570

Step - 2:

Option price on expiry = max(16.5 - 14.5 , 0)*0.430 = 2*0.430

Option price on expiry = max(14 - 14.5 , 0)*0.570 = 0*0.570

Option price on maturity = 2*0.430 + 0*0.570 = $0.860

[we can also find present value of option:

Present value = 0.860 / e^rt

= 0.860 / e^(0.06*(1/12))

= 0.8557]