The correct answer is D.

Taking a long position of the same size in a live cattle futures contract with the same delivery date is the most appropriate method to terminate a short position in futures contracts. This is because futures contracts are standardized agreements that are traded on an exchange. When an investor takes a short position in a futures contract, they are agreeing to sell the underlying asset at a specific price on a specific date in the future. If the investor later decides to terminate this position, they can do so by taking an exactly opposite position (a long position) in the same futures contract with the same maturity date. This effectively cancels out the original short position, allowing the investor to exit the contract without having to deliver the physical goods. This method is commonly used in futures trading and is considered the most efficient and cost-effective way to terminate a futures contract.

Choice A is incorrect. Physically delivering the cattle from Mumbai to the long party in Chicago would not terminate the futures contract. The futures contract is a legal agreement to buy or sell a particular commodity at a predetermined price at a specified time in the future. Physical delivery of cattle does not nullify this agreement.

Choice B is incorrect. Taking a new short position of the same size in a live cattle futures contract with a different delivery date would not terminate the existing short position but rather create an additional one. This action would increase, not decrease, Vikram's exposure to live cattle prices.

Choice C is incorrect. Off-exchange bilateral settlement is not permitted for exchange-traded futures contracts. All transactions must go through the exchange to maintain standardization, guarantee performance, and ensure proper clearing through the exchange's clearinghouse.