Explanation:
According to the delta-normal approach:
VaR of a derivative position = Delta × VaR of the underlying asset
The 1-day 99% VaR of 1 share of the underlying is USD 1.4097:
VaR of underlying = 1.21% × 2.33 × 50 = 1.4097
VaR of one option = 0.5 × 1.4097 = 0.7049
Thus, for 500 options, we have,
Total VaR of the position = 0.7049 × 500 = 352.43
Option A is incorrect. This is the result when delta is not applied in the formula:
VaR = 1.4097 × 500 = 704.85
Option B is incorrect. This is the result obtained when we use 2.58 as the z-value instead of 2.33:
VaR = 0.5 × 1.21% × 2.58 × 50 × 500 = 390.23
Option C is incorrect. This is the result obtained when the strike price is used in the calculation instead of the stock price:
VaR = 0.5 × 1.21% × 2.33 × 50 × 500 = 317.17317
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Q.33 Hans Zimmer is a portfolio manager at ABC firm. The firm wishes to buy 500 call options on a stock whose current price is USD 50 with a daily volatility of 1.21%. The strike price is USD 45, the delta of the option is 0.5, and each call option costs USD 5. If Hans wishes to calculate the VaR of the position using the delta-normal approach, what will be the 1-day 99% VaR?
A
704.85.
B
390.23.
C
317.17.
D
352.43.
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