The correct answer is C, which is USD 13,715. To determine the 1-day 99% Value-at-Risk (VaR) for the portfolio, we first need to understand the composition of the portfolio and the characteristics of the options and forward contracts it contains. The portfolio consists of:

• 5,000 deep in-the-money call options on TUV, which have a delta close to 1, meaning they behave almost like the underlying stock.
• 20,000 deep out-of-the-money call options on TUV, which have a delta close to 0, indicating they have minimal exposure to the underlying stock's price movements.
• 10,000 forward contracts on TUV, each with a delta of 1, similar to the deep in-the-money calls.

Given these details, the net delta of the portfolio is calculated as follows: $\text{Net Delta (Dp)} = (1 \times 5,000) + (0 \times 20,000) + (1 \times 10,000) = 15,000$

This indicates that the portfolio has a significant exposure to the underlying stock TUV, equivalent to holding 15,000 shares.

The next step is to calculate the 1-day VaR using the following formula: $\text{VaR} = \alpha \times S \times Dp \times \sigma \times \sqrt{\frac{1}{T}}$

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.
• $\sigma$ is the volatility of TUV, which is 12% per year or 0.12.
• $T$ is the time in years, which for a 1-day period is $\frac{1}{252}$ (assuming 252 trading days in a year).

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

This calculation provides an estimate of the maximum loss that the portfolio could experience with 99% confidence within a single trading day. The result is rounded to USD 13,715, which corresponds to option C in the given choices.