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%.

1. Please solve the futures call option premium based on the fact that at time zero, the cost of acquiring a portfolio is equal to the value of the portfolio.

(1 mark)

Answer 1

Given

Current Price of the Stock = 15$ per share

Tenure of the option = 1 month

Upper movement of price in future(u) = (16.5-15)/15 = 0.1

Downward movement of price in future (d) = (15-14)/15 = 0.067

Strike Price (K) = 14.5 $

Risk Free Rate(r) = 6%

Under Direct Formula Method

fo = {[(fu-fd) + e^(-rt)*(ufd-dfu)] / (u-d)}

fu = payoff from the option contract if the price goes up = upper price-Strike price= 16.5-14.5 = 2$

fd = payoff from the option contract if the price goes down = 0$

Since it is call option, it will be executed only when the price goes up, therefore payoff will be when price goes up.

The value of option = {[(2-0) + e^(-0.06*1/12)*((0.10*0 - 0.067*2))]/(0.10-0.067)}

= [2 + (0.9950)*(-0.134)]/0.033

= 1.86667/0.033

= 56.5658$