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Answer: Option D
## Explanation The delta-normal model works best for linear portfolios and serves as an approximation for non-linear portfolios such as option positions. This approximation is reasonable when curvature (as measured by gamma) is low, but becomes less accurate as gamma increases. **Key Analysis:** - **Gamma characteristics**: Gamma is lower for options that are deep in-the-money or deep out-of-the-money compared to at-the-money options - **Current stock price**: USD 79 - **Option analysis**: - Option A (Call, Strike 75): In-the-money (current price 79 > strike 75) - Option B (Call, Strike 80): Near at-the-money (current price 79 ≈ strike 80) - Option C (Put, Strike 80): Near at-the-money (current price 79 ≈ strike 80) - Option D (Put, Strike 95): Deep in-the-money (current price 79 < strike 95) **Why Option D is best for delta-normal VaR:** - Option D is deep in-the-money, resulting in the lowest gamma among all positions - Gamma is equal for call or put options with identical characteristics - Lower gamma means less curvature risk, making the linear approximation of delta-normal VaR more accurate - Options A, B, and C are closer to at-the-money and therefore have higher gamma, making delta-normal VaR less suitable The delta-normal VaR will offer the best approximation of true risk for Option D due to its minimal curvature risk.
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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