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.