(Continued from Q6) If the actual put premium is $4.5 instead of its appropriate level, which of the following statement is false about making an arbitrage profit from the mispricing?

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BlackTom AI · Accepted Answer

To analyze the statements about arbitrage profit from a put premium mispricing, we need to consider how mispricing drives potential positions and profits.
Option A: 'You should buy the leveraged stock portfolio.' This suggestion mirrors a common arbitrage approach where one might construct a hedged position using leveraged exposure to replicate or hedge the underlying risk while exploiting mispricing in options. The rationale here is that if the put premium is mispriced relative to the theoretical value, going long a hedged or leveraged stock sleeve could be part of a strategy to capture the discrepancy, depending on the overall payoff structure and hedging costs. There is no inherent reason this would always be invalid on its own.
Option B: 'You should sell the option portfolio.' Selling the option portfolio is another typical arbitrage technique when options appear overvalued relative to their theoretical value or when a static hedge can be established to lock in risk-free profit. If the mispricing means the puts are too expensive, selling the option portfolio could be a logical component of an arbitrage strategy, subject to margin, gamma, and vega considerations and the accompanying hedges.
Option C: 'The arbitrage profit should be $0.98.' This statement asserts a fixed, predetermined profit amount. In real arbitrage scenarios, the exact profit is not a constant number; it depends on the magnitude of the mispricing, the precise hedge, transaction costs, financing, and any changes in the underlying or implied volatility during the trade. Therefore, asserting a fixed profit like 0.98 is unlikely to be universally true and can be misleading.
Option D: 'None of the above.' Choosing this would imply that both A and B are invalid or that C is not the false statement, depending on the intended interpretation. Since arbitrage strategies are highly context-specific, and one cannot categorically rule out long-levered hedges or short option portfolios as potential components, this option requires careful consideration against the other statements and the particular mispricing scenario at hand.
In light of these points, the core issue is that arbitrage profits are contingent on the scale of mispricing and the cost structure of the trade; claiming a universal fixed profit amount is the least defensible assertion, while the other two options describe plausible actions in arbitrage setups, albeit depending on the precise market context. The false statement is thus the one that asserts a fixed profit amount without regard to trade-specific variables.

MFIN8860.01 Summer 2025 Derivatives and Risk Analytics [Jiang] Homework 8

(Continued from Q6) If the actual put premium is $4.5 instead of its appropriate level, which of the following statement is false about making an arbitrage profit from the mispricing?

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