The correct answer to the question is C, which is USD 13,715. To understand why, we need to analyze the portfolio and calculate the Value-at-Risk (VaR) using the given parameters.

The portfolio consists of:

• 5,000 deep in-the-money call options on TUV.
• 20,000 deep out-of-the-money call options on TUV.
• 10,000 forward contracts on TUV.

The stock TUV is trading at USD 52, and the volatility is 12% per year. The options and forward contracts are assumed to be on one share each.

Here's the breakdown:

• Deep in-the-money call options have a delta close to 1, meaning they behave almost like the underlying stock.
• 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.
• Forward contracts also have a delta of 1, as they obligate the holder to buy or sell the underlying asset at a predetermined price.

The net delta of the portfolio (Dp) is calculated as follows:

• 5,000 in-the-money calls contribute a delta of 5,000 (1 * 5,000).
• 20,000 out-of-the-money calls contribute a delta of 0 (0 * 20,000).
• 10,000 forward contracts contribute a delta of 10,000 (1 * 10,000).

So, Dp = 5,000 + 0 + 10,000 = 15,000.

The portfolio is approximately gamma neutral, which means it has minimal curvature in its price response to changes in the underlying asset's price.

The 1-day 99% VaR is calculated using the formula: α * S * Dp * σ * sqrt(1/T)

Where:

• α is the z-score corresponding to the 99% confidence level (2.326).
• S is the price per share of stock TUV (USD 52).
• Dp is the delta of the position (15,000).
• σ is the volatility of TUV (0.12).
• T is the time in years for the VaR calculation (1 trading day / 252 trading days in a year).

Plugging in the values: VaR = 2.326 * 52 * 15,000 * 0.12 * sqrt(1/252) = USD 13,714.67

This calculation provides an estimate of the maximum loss the portfolio could experience with 99% confidence within one trading day. The closest option to this calculated value is C, USD 13,715.