Answer: selling short the underlying and investing the proceeds at the risk-free rate.

## Explanation When a call option is overvalued relative to the binomial model, investors can create an arbitrage opportunity by: 1. **Selling the overvalued call option** - This generates immediate cash inflow. 2. **Creating a synthetic short position in the call option** - This involves selling short the underlying asset and investing the proceeds at the risk-free rate. ### Why Option B is Correct: According to put-call parity and binomial option pricing theory, when a call option is overpriced: - **Sell the call option** (overvalued) - **Create a synthetic short call position** by: - Short selling the underlying stock - Investing the proceeds from the short sale at the risk-free rate This creates a risk-free arbitrage position because: - The synthetic short call (short stock + risk-free investment) should have the same value as the short call option - Since the actual call option is overvalued, selling it and buying the synthetic short position creates an immediate profit - The position is risk-free and should earn more than the risk-free rate ### Why Other Options are Incorrect: **Option A (buying the underlying)**: This would create a covered call position, which doesn't exploit the overvaluation properly. **Option C (buying the underlying and borrowing)**: This creates a leveraged long position in the underlying, which doesn't hedge the short call position properly. ### Arbitrage Mechanics: The arbitrageur would: 1. Sell the overvalued call option for price C 2. Short sell the underlying stock for price S 3. Invest S at the risk-free rate At expiration: - If stock price > strike price: The call option will be exercised, and the arbitrageur delivers the stock (from short position) - If stock price ≤ strike price: The call expires worthless, and the arbitrageur buys back the stock to cover the short position In both cases, the arbitrageur earns a risk-free profit equal to the difference between the overvalued call price and the fair value from the binomial model.

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