Question

suppose that you are looking at a stock that is currently traded at $25. the put with a strike price of $22 is traded at $0.48 and the call with a strike price of $22 is traded at $4.89. both options will expire in 3 months. if the risk-free rate is 4 percent, does an arbitrage exist? if so, what is the trading strategy to implement to extract benefit from the arbitrage?

Answer 1

Arbitrage is a financial strategy that takes advantage of price differences in different markets to make a riskless profit. In this scenario, an arbitrage opportunity exists because the call option is undervalued compared to the put option. The trading strategy to extract benefit from the arbitrage involves buying the undervalued call option, selling the put option, short selling the stock, and investing in a risk-free bond at the risk-free rate.

Step-by-step explanation:

Arbitrage is a financial strategy that takes advantage of price differences in different markets to make a riskless profit. In this scenario, an arbitrage opportunity exists because the call option is undervalued compared to the put option. Here's the trading strategy to extract benefit from the arbitrage:

1. Buy the undervalued call option with a strike price of $22 for $4.89.
2. Sell the put option with a strike price of $22 for $0.48.
3. Short sell the stock at the current market price of $25.
4. Invest the proceeds in a risk-free bond at the risk-free rate of 4%.
5. After 3 months, if the stock price is above $22, exercise the call option and buy back the short position.
6. If the stock price is below $22, let the put option expire and buy back the short position at the lower stock price.
7. Replicate this strategy until expiration to keep profiting from the arbitrage opportunity.