VaR: Exchange Rate Risk and Jump Risk

Table 2

Parameter estimation of dynamic processes of asset returns and exchange rate returns in various periods.

Security and exchange rate	Period I		Period II
	2004/1/1–2007/7/31		2007/8/1–2009/11/27
	𝜇𝑖	𝜎𝑖	𝜇𝑖	𝜎𝑖
TSMC	0.1959	0.2463	0.0331	0.1735
MSFT	0.1858	0.1799	0.0929	0.4102
TAIEX	0.0668	0.0816	−0.0263	0.1394
S&P 500	0.0387	0.0497	−0.0495	0.1484
NTD/USD	−0.0096	0.0397	−0.0052	0.0475

Assume the number of jumps is ten. Given 𝑢_𝜋=0.05, 𝜎^2𝜋=0.001, and 𝜆=0.03 for Period I, and 𝑢_𝜋=0.055, 𝜎^2𝜋=0.002, and 𝜆=0.035 for Period II, 𝜇_𝑖 and 𝜎_𝑖 demonstrate the estimation of drift terms and volatilities of asset (index) returns and foreign exchange returns for 𝑖=𝑑₁, 𝑓₁, and 𝑒₁, respectively.