Financial Risk Manager Part 1

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Explanation:

p_{\text{up}} = \frac{e^{(r_{\text{USD}} - r_{\text{EUR}}) \times \Delta t}}{u - d} = \frac{e^{(0.02 - 0.005) \cdot 0.25} - e^{-0.25 \sqrt{0.25}}}{e^{0.25 \sqrt{0.25}} - e^{-0.25 \sqrt{0.25}}} = 0.4838

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

Index Price	$e^{0.25\sqrt{0.25}} = 0.3031$
Option Strike Price	1.1
Option Value	0.2031

Index Price	1.15
Option Strike Price	1.1
Option Value	?

→

Index Price	$e^{-0.25\sqrt{0.25}} = 0.0149$
Option Strike Price	1.1
Option Value	0

Price at Node A = $(0.2031 \times 0.4838 + 0 \times (1 - 0.4838)) \, e^{-2.0\% \times \frac{3}{12}} = 0.0978$

Explanation:

p_{\text{up}} = \frac{e^{(r_{\text{USD}} - r_{\text{EUR}}) \times \Delta t}}{u - d} = \frac{e^{(0.02 - 0.005) \cdot 0.25} - e^{-0.25 \sqrt{0.25}}}{e^{0.25 \sqrt{0.25}} - e^{-0.25 \sqrt{0.25}}} = 0.4838

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

Index Price	$e^{0.25\sqrt{0.25}} = 0.3031$
Option Strike Price	1.1
Option Value	0.2031

Index Price	1.15
Option Strike Price	1.1
Option Value	?

→

Index Price	$e^{-0.25\sqrt{0.25}} = 0.0149$
Option Strike Price	1.1
Option Value	0

Price at Node A = $(0.2031 \times 0.4838 + 0 \times (1 - 0.4838)) \, e^{-2.0\% \times \frac{3}{12}} = 0.0978$

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Last updated: May 21, 2026 at 04:19

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