Explanation:
D is correct. The delta-normal model works best for linear portfolios, and is an approximation for non-linear portfolios such as option positions. This approximation is reasonable when curvature (as measured by gamma) is low, but as gamma becomes larger, this approximation breaks down.
Gamma is lower for an option that is deep in-the-money or deep out-of-the-money than it is for an at-the-money option. Of the four options under consideration:
As discussed in Section 16.4 of the text, gamma is equal for call or put option positions that are otherwise identical. Therefore, option D, being deep in-the-money, has the lowest gamma among the four options, and its delta-normal VaR will offer the best approximation of its true risk.
A, B, and C are incorrect per the explanation for D above — these options are closer to at-the-money, so they have higher gamma, making the delta-normal approximation less accurate.
Learning Objective: Describe the limitations of the delta-normal method.
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Q-96. A risk analyst at a derivatives trading firm is estimating the VaR of several options positions. The analyst considers using the delta-normal model for these estimates, but acknowledges this model has limitations that could make its application less suitable under certain situations. The analyst focuses on the following positions in options on stock LCO:
| Option | Type | Strike price (USD) |
|---|---|---|
| A | Call | 75 |
| B | Call | 80 |
| C | Put | 80 |
| D | Put | 95 |
The current price of stock LCO is USD 79, and all four options expire in exactly 1 month. For which of these positions would delta-normal VaR best reflect its risk?
A
Option A
B
Option B
C
Option C
D
Option D
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