Using initial inputs:

$$p_{\text{up}} = \frac{(e^{(r \times \Delta t)} - d)}{(u - d)} = \frac{(e^{3\%} - e^{-0.3})}{(e^{0.3} - e^{-0.3})} = 0.4756$$

The figure below shows the stock price and the corresponding option’s intrinsic value at each node.

• Node A:

  • Index Price: 100
  • Option’s Strike price: 90
  • Option’s Value: ?

• Node B:

  • Index Price: 134.99
  • Option’s Strike price: 90
  • Option’s Value: –

• Node C:

  • Index Price: 74.08
  • Option’s Strike price: 90
  • Option’s Value: 15.92

Price at A = $(0 \times 0.4756 + 15.92 \times (1 - 0.4756)) \times e^{(-3.0\%)} = 8.10$

Using corrected inputs:

$$u = e^{0.50} = 1.6487$$ $$d = e^{-0.50} = 0.6065$$ $$p_{\text{up}} = \frac{(e^{3\%} - 0.6065)}{(1.6487 - 0.6065)} = 0.4068$$

• Node A:

  • Index Price: 100
  • Option’s Strike price: 90
  • Option’s Value: ?

• Node B:

  • Index Price: 164.87
  • Option’s Strike price: 90
  • Option’s Value: 0

• Node C:

  • Index Price: 60.65
  • Option’s Strike price: 90
  • Option’s Value: 29.35

Price at A = $(0 \times 0.4068 + 29.35 \times (1 - 0.4068)) \times e^{(-3.0\%)} = 16.90$

Difference = 16.90 - 8.10 = +USD 8.80