Journal of Probability and Statistics

Research Article

VaR: Exchange Rate Risk and Jump Risk

Table 1

Sample mean and standard deviation of daily log returns of securities and exchange rates in various periods.
Period IPeriod II
2004/1/1–2007/7/312007/8/1–2009/11/27
Variables 𝐸 [ 𝑑 ( l n 𝐻 𝑡 ) ] 𝜎 ( 𝑑 l n 𝐻 𝑡 ) 𝐸 [ 𝑑 ( l n 𝐻 𝑡 ) ] 𝜎 ( 𝑑 l n 𝐻 𝑡 )
Panel A: sample mean and standard deviation of daily log returns
TSMC0.0006566790.0155177160.0000712540.010939352
MSFT0.0000645210.0117056470.0000349940.025837488
TAIEX0.0002515630.005154917−0.0001432390.008799451
S&P 5000.0001485010.003132479−0.0002402380.025837488
NTD/USD−0.0000414580.002526791−0.0000252630.003041025
Panel B: sample mean and variance of log returns per annum
TSMC0.1654831080.0606814760.0179557560.030156694
MSFT0.016259292 0.0345295870.0088182360.168229098
TAIEX0.063393876 0.006696439−0.0360864110.019510445
S&P 5000.0374222520.002472731−0.0605399760.02203105
NTD/USD−0.010447416 0.001608938−0.0064582560.002330454
Note that 𝐸 [ 𝑑 ( l n 𝐻 𝑡 ) ] and 𝜎 ( 𝑑 l n 𝐻 𝑡 ) represent the sample means and standard deviations of daily log returns of domestic assets (indices), foreign assets (indices), and exchange rates for all 𝐻 𝑡 = 𝐴 𝑑 1 , 𝑡 , 𝐴 𝑓 1 , 𝑡 , 𝑒 1 , 𝑡 , respectively. Panel B displays the sample means and variances of domestic assets (indices), foreign assets (indices), and exchange rates per annum all multiplied by 252 from Panel A, respectively.