The portfolio in question consists of a mix of options and forward contracts on TUV, a non-dividend paying stock. The options include 5,000 deep in-the-money call options and 20,000 deep out-of-the-money call options, while the portfolio also contains 10,000 forward contracts. To estimate the 1-day 99% Value-at-Risk (VaR) of the portfolio, we must first understand the delta of each component:

1. Deep in-the-money call options have a delta close to 1, meaning they behave almost like the underlying stock.
2. Deep out-of-the-money call options have a delta close to 0, meaning they have minimal exposure to the underlying stock's price movements.
3. Forward contracts also have a delta of 1, as they obligate the holder to buy or sell the underlying asset at a predetermined price.

Given these deltas, the net delta of the portfolio is calculated as follows:

• The 5,000 deep in-the-money calls contribute a delta of 5,000 (since each option has a delta of approximately 1).
• The 20,000 deep out-of-the-money calls contribute a delta of 0.
• The 10,000 forward contracts contribute a delta of 10,000.

This results in a total delta (Dp) of 15,000 for the portfolio, which is approximately gamma neutral, meaning it has a relatively stable delta across small price changes in TUV.

The 1-day VaR at a 99% confidence level can be estimated using the following formula: $\text{VaR} = a \times S \times Dp \times g \times \sqrt{\frac{1}{T}}$

Where:

• $a$ is the z-score corresponding to the 99% confidence level, which is 2.326.
• $S$ is the price per share of TUV, which is USD 52.
• $Dp$ is the delta of the position, which is 15,000.
• $g$ is the volatility of TUV, which is 12% per year.
• $T$ 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: $\text{VaR} = 2.326 \times 52 \times 15,000 \times 0.12 \times \sqrt{\frac{1}{252}}$ $\text{VaR} = 13,714.67$

Thus, the closest amount to the 1-day 99% VaR of the portfolio is USD 13,715, which corresponds to option C. This calculation provides an estimate of the maximum loss that the portfolio could experience in one day, with a 99% confidence level, assuming normal market conditions and a lognormal distribution of returns.