The binomial model can modified to incorporate the unique characteristics of options on futures. Of note is the fact that futures contracts are largely considered cost-free to initiate, and therefore in a risk-neutral environment, they are zero-growth instruments. The probability of an up-move is therefore given by:

$$p = \frac{e^{rT} - d}{u - d} = \frac{1.0305 - e^{-0.21}}{e^{0.21} - e^{-0.21}} = 0.5197$$

At t=0:
Index price = USD 88
Option’s strike price = USD 85

At t=1, we have the up move and the down move:
For the up move, the index price is USD $88 \times e^{0.21} =$ USD 108.56; the option’s strike price is USD 85 and the option value is therefore USD $108.56 - 85 =$ USD 23.56
For the down move, the index price is USD $88 \times e^{-0.21} =$ USD 71.33. Given that the index price (USD 71.33) is below the strike price (USD 85), the option is valueless (value of zero).

Finally, we need to weight both values to get the price of the option at t=0:
Price at T0 = $(23.56 \times 0.5197 + 0 \times (1 - 0.5197)) \times e^{-3.0\%} = 11.88$