Answer: sell the call option, buy stock and lend cash.

## Explanation To identify the arbitrage opportunity, we need to check if the call option is mispriced relative to its theoretical value using the binomial model. **Given data:** - Strike price (K) = 55.00 - Current stock price (S₀) = 50.00 - Call price (C₀) = 13.50 - Up move probability (π) = 0.60 - S⁺ = 67.80, S⁻ = 27.05 - C⁺ = 21.52, C⁻ = 0.00 - Risk-free rate (r) = 3.00% **Calculate theoretical call value:** First, calculate the risk-neutral probability: \[ p = \frac{(1+r) - d}{u - d} \] Where: \[ u = \frac{S⁺}{S₀} = \frac{67.80}{50.00} = 1.356 \] \[ d = \frac{S⁻}{S₀} = \frac{27.05}{50.00} = 0.541 \] \[ p = \frac{1.03 - 0.541}{1.356 - 0.541} = \frac{0.489}{0.815} = 0.60 \] **Theoretical call value:** \[ C₀ = \frac{p \times C⁺ + (1-p) \times C⁻}{1+r} = \frac{0.60 \times 21.52 + 0.40 \times 0}{1.03} = \frac{12.912}{1.03} = 12.54 \] **Arbitrage analysis:** - Theoretical value = 12.54 - Market price = 13.50 - The call is **overpriced** by 0.96 **Arbitrage strategy:** Since the call is overpriced, we should: 1. **Sell the call option** (receive 13.50) 2. **Buy the underlying stock** (hedge the short call position) 3. **Lend cash** (invest the remaining proceeds at risk-free rate) This creates a risk-free profit because we're selling the overpriced call and creating a synthetic long position that replicates the call's payoff at a lower cost.

Author: LeetQuiz Editorial Team