Financial Risk Manager Part 1

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Explanation:

This question involves binomial tree modeling with dividends.

Initial assumptions:

σ = 0.2840 (volatility)
Δt = 1
u = e^{σ√Δt} = e^{0.2840} = 1.32950
d = 1/u = 0.75216
p = d = 0.50 (risk-neutral probability)

With dividend (q):

p = [e^{(r-q)Δt} - d] / (u - d) = 0.46427
d = 1 - p = 1 - 0.46427 = 0.53573

Increase calculation:

Initial d = 0.75216
New d = 0.53573
Increase = (0.53573 - 0.75216) / 0.75216 = -0.21643 / 0.75216 = -0.2877 = -28.77%

Wait, the text says "increase is about 3.570%" but the calculation shows a decrease. This suggests there might be a different interpretation or the text contains an error. The correct interpretation should be that the down probability increases from 0.50 to 0.53573, which is an increase of 7.146%.

Explanation:

This question involves binomial tree modeling with dividends.

Initial assumptions:

σ = 0.2840 (volatility)
Δt = 1
u = e^{σ√Δt} = e^{0.2840} = 1.32950
d = 1/u = 0.75216
p = d = 0.50 (risk-neutral probability)

With dividend (q):

p = [e^{(r-q)Δt} - d] / (u - d) = 0.46427
d = 1 - p = 1 - 0.46427 = 0.53573

Increase calculation:

Initial d = 0.75216
New d = 0.53573
Increase = (0.53573 - 0.75216) / 0.75216 = -0.21643 / 0.75216 = -0.2877 = -28.77%

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Q-28.

Under the initial set of assumptions, $u = e^{\sigma\sqrt{\Delta t}} = e^{0.2840\sqrt{1}} = 1.32950$ and $d = 1 / 1.32950 = 0.75216$ , such that $p = d = 0.50$ .

If the dividend is included, then $p = \frac{e^{(r-q)\Delta t} - d}{u - d} = 0.46427$ . Therefore, $d = 1 - 0.46427 = 0.53573$ , and the increase is about 3.570%.

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