* Current VaR: The bank has an existing VaR estimate of $100 million.
* Standalone VaR for New Transaction: The standalone VaR of the new transaction is $5 million.
* Correlation with Current Portfolio: The correlation of the new transaction with the current portfolio is
0.35.
* Formula for Combined VaR:
New VaR=(Current VaR2)+(Standalone VaR2)+2×Correlation×Current VaR×Standalone VaR\text{New VaR} = \sqrt{(\text{Current VaR}^2) + (\text{Standalone VaR}^2) + 2 \times \text{Correlation} \times
\text{Current VaR} \times \text{Standalone
VaR}}New VaR=(Current VaR2)+(Standalone VaR2)+2×Correlation×Current VaR×Standalone VaR Plugging in the values:
New VaR=(1002)+(52)+2×0.35×100×5=10000+25+350=10375101.86\text{New VaR} = \sqrt{(100^2) + (5^2) + 2 \times 0.35 \times 100 \times 5} = \sqrt{10000 + 25 + 350} = \sqrt{10375} \approx
101.86New VaR=(1002)+(52)+2×0.35×100×5=10000+25+350=10375101.86
ReferencesSource: How Finance Works

Running trades through a clearinghouse provides several advantages for the small bank, including:
* Eliminating the Collateral Requirement:
* The clearinghouse nets positions and reduces the need for bilateral collateral postings.
* Protecting Against Increases in Future Collateral Demands:
* Centralized clearing reduces the potential for unexpected margin calls as prices fluctuate.
* Protecting Against the Risk of the Failure of One of the Large Banks:
* The clearinghouse acts as a central counterparty, reducing the impact if one large bank fails.
However, the clearinghouse does not specifically address option hedging risks or alter margin requirements directly related to options. Therefore, the correct answer is that running trades through a clearinghouse does not achieve the objective of mitigating option hedging risks and altering margin requirements.
ReferencesSource: How Finance Works

When a bank hedges with futures contracts, it needs to maintain margin accounts which are settled daily to reflect market changes:
* Margin Calls: If the market moves against the position of the futures, the bank must add funds to the margin account to cover potential losses. This can create significant liquidity risk if large sums are needed quickly.
* Daily Settlements: Futures markets require daily mark-to-market settlements which means that any adverse movement in prices necessitates immediate liquidity to meet the margin requirements.
* Market Volatility: In times of high volatility, the daily margin requirements can be substantial, potentially causing a scramble for liquidity if the bank has not pre-arranged sufficient liquidity buffers.
Thus, the need for daily margin settlements exposes the bank to liquidity risk as it must be able to provide cash on short notice.References: How Finance Works, relevant sections on liquidity risks in derivative markets.