Solution to Assignment Nr. E1
FRM20ID: 695176
(Assignment under consideration)
(your six digit number)
Relevant parameters based on my FRM20ID:
_____________________________________________________________________________
Q1: Return = 10%, Volatility = 50%, Dividend yield = 7%, Current value share = 76 euro, Confidence
interval = 99% Q2: Expected return: 0,1% , Return volatility: 5%, Weekly dividend: 0,07%, Current
value share: 76 euro, Strike price : 90 euro, Weeks: 16
Insert your solution here:
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1a. ln(𝑆0.5 year ) ∼ 𝑁 ((0.1 − 0.07 − 2 ∗ 0,52 ) ∗ 0.5, 0.52 ∗ 0.5)
ln(𝑆0.5 year ) ∼ 𝑁 (−0.095, 0.125)
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1b. ln(𝑆0.5 year ) ∼ 𝑁 ((0.1 − 0.07 − 2 ∗ 0,52 ) ∗ 0.5, 0.52 ∗ 0.5)
ln(𝑆0.5 year ) ∼ 𝑁 (−0.095, 0.125)
Confidence interval of 99% results in 2,58 standard deviations of mean in case of normally distributed
variable.
𝑆0.5 year
−0.095 − 2.58 ∗ √0.125 ≤ ln (
𝑒 −1,01 ≤
𝑆0.5
76
76
) ≤ −0.095 + 2.58 ∗ √0,125
≤ 𝑒 0.817
27,76 ≤ 𝑆0.5 ≤ 172,07
Prices on a 99% confidence interval range between 27,75 Euro to 172.07 Euro.
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2a. ln(𝑆16 ) ∼ 𝑁 ((0.001 − 0.0007 − 2 ∗ 0,052 ) ∗ 16, 0.052 ∗ 16)
ln(𝑆16 ) ∼ 𝑁(−0.0152, 0.04)
2b. Prob (St > K) = 1 – Prob (St < L)
𝑃𝑟𝑜𝑏 (𝑆𝑡 > 𝐾) = 1 − 𝑁
ln(90)−ln(76)+(0.001−0.0007−0.5∗0.052 )∗16
0.05∗√16
Prob (St > K) = 1- N (0.769)
Prob (St > K) = 0.27935
The probability that the share value exceeds 90 Euros in 16 weeks is 27,94%
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05 Mar. 22