The real-world probabilities of market moving up or down are never encountered during the calculation of the arbitrage price. This is because arbitrage pricing is based on the principle of no-arbitrage, which assumes that there are no opportunities to make risk-free profits. In this context, the real-world probabilities of market movements are irrelevant. The arbitrage price is determined by the prices of the underlying assets and the risk-free rate of return, not by the probabilities of market movements. Therefore, these probabilities do not enter into the calculation of the arbitrage price.

Choice B is incorrect. Real-world probabilities are not always encountered while calculating the arbitrage price. The arbitrage pricing theory relies on the assumption of no-arbitrage conditions, which means that it does not require any information about the real-world probabilities of market moving up or down.

Choice C is incorrect. The statement that real-world probabilities are sometimes encountered during the calculation of arbitrage price is misleading. In fact, these probabilities do not play a role in determining the arbitrage price as per no-arbitrage conditions.

Choice D is incorrect. Real-world probabilities are neither partially nor fully considered in calculating the arbitrage price under no-arbitrage conditions, making this choice invalid.

Things to Remember

• Arbitrage pricing is based on the principle of no-arbitrage, which assumes that there are no opportunities to make risk-free profits.
• The arbitrage price is determined by the prices of the underlying assets and the risk-free rate of return, not by the probabilities of market movements.
• Real-world probabilities of market movements are irrelevant in the calculation of the arbitrage price.