NO.PZ2024030508000096
问题如下:
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:
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?
选项:
A.Option A B.OptionB C.Option C D.Option D解释:
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 bigger this is no longer true.
Gamma is lower for an option that is in-the-money or out-of-the-money than it is for an at-the-money option. Of the four options under consideration, option D is deep in-the-money, while options A, B, and C are closer to at-the-money. (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 has the lowest gamma, and its delta-normal VaR will offer the best approximation of its true risk out of the options given.
A, B, and C are incorrect per the explanation for D above.
Learning Objective: Describe the limitations of the delta-normal method.
Define and describe vega, gamma, theta, and rho for option positions and calculate the gamma and vega of an option.
Reference: Global Association of Risk Professionals, Valuation and Risk Models (New York, NY: Pearson, 2023). Chapter 2. Calculating and Applying VaR [VRM–2]
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