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Answer: USD 13,715
## Explanation To calculate the 1-day 99% VaR of the portfolio, we need to map the portfolio to a position in the underlying stock TUV using delta approximation: **Delta Analysis:** - Deep in-the-money call options: delta ≈ 1 - Deep out-of-the-money call options: delta ≈ 0 - Forward contracts: delta = 1 **Net Portfolio Delta (D_p):** - 5,000 deep ITM calls × delta 1 = 5,000 - 20,000 deep OTM calls × delta 0 = 0 - 10,000 forwards × delta 1 = 10,000 - **Total D_p = 15,000** **VaR Calculation Parameters:** - Confidence level (99%): α = 2.326 - Stock price: S = USD 52 - Portfolio delta: D_p = 15,000 - Annual volatility: σ = 0.12 - Trading days: 252 - Time horizon: 1 day **1-day VaR Formula:** ``` VaR = α × S × D_p × σ × √(1/252) ``` **Calculation:** ``` VaR = 2.326 × 52 × 15,000 × (0.12/√252) = 2.326 × 52 × 15,000 × (0.12/15.8745) = 2.326 × 52 × 15,000 × 0.00756 = 2.326 × 52 × 113.4 = 2.326 × 5,896.8 = USD 13,714.67 ``` The portfolio is approximately gamma neutral, so delta approximation is appropriate. The closest amount to USD 13,714.67 is **USD 13,715**.
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A fund manager owns a portfolio of options on TUV, a non-dividend paying stock. The portfolio is made up of 5,000 deep in-the-money call options on TUV and 20,000 deep out-of-the-money call options on TUV. The portfolio also contains 10,000 forward contracts on TUV. Currently, TUV is trading at USD 52. Assuming 252 trading days in a year, the volatility of TUV is 12% per year, and that each of the option and forward contracts is on one share of TUV, which of the following amounts would be closest to the 1-day 99% VaR of the portfolio?
A
USD 11,557
B
USD 12,627
C
USD 13,715
D
USD 32,000
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