The correct answer is C, which is USD 13,715. The explanation for this is rooted in the delta-mapping technique used to determine the Value-at-Risk (VaR) for the portfolio. The portfolio consists of deep in-the-money call options, deep out-of-the-money call options, and forward contracts, all on the non-dividend paying stock TUV.

To calculate the 1-day 99% VaR, we first determine the net delta (Dp) of the portfolio:

• Deep in-the-money calls have a delta close to 1, contributing 5,000 * 1 = 5,000 to the net delta.
• Deep out-of-the-money calls have a delta close to 0, contributing 0 * 20,000 = 0 to the net delta.
• Forward contracts have a delta of 1, contributing 10,000 * 1 = 10,000 to the net delta.

The net delta (Dp) is therefore 5,000 + 0 + 10,000 = 15,000.

Next, we use the formula for calculating VaR: $\text{VaR} = \alpha \times S \times Dp \times \gamma \times \sqrt{\frac{1}{T}}$

Where:

• $\alpha$ is the z-score corresponding to the 99% confidence level, which is 2.326.
• $S$ is the price per share of stock TUV, which is USD 52.
• $Dp$ is the delta of the position, which is 15,000.
• $\gamma$ is the volatility of TUV, which is 12% or 0.12.
• $T$ is the time period in days, which is 1 day for a 1-day VaR.

Plugging in the values, we get: $\text{VaR} = 2.326 \times 52 \times 15,000 \times 0.12 \times \sqrt{\frac{1}{252}}$ $\text{VaR} = 2.326 \times 52 \times 15,000 \times 0.12 \times \sqrt{0.00396825}$ $\text{VaR} = 2.326 \times 52 \times 15,000 \times 0.12 \times 0.06325$ $\text{VaR} = USD 13,714.67$

This calculation provides the estimated maximum loss with 99% confidence over a one-day period, which is closest to option C, USD 13,715.