There are three assets in the economy, stock, money, and call option. The stock price tomorrow can be either 5 or 15 depending on circumstances. The money price tomorrow is 1 independent of the economy. The call option has a strike price of 10 (if you own one unit of the call option, you are entitled to purchase a share of stock tomorrow at the strike price). Suppose today’s prices for a share of stock is 12, for money is 1, and for an unit of the call option is 4. Question: Is there an arbitrage (A portfolio that has a negative price today and nonnegative value in all circumstances tomorrow)? If an arbitrage exists, please find one. If no arbitrage exists, explain why.
An arbitrage is a portfolio that has a negative or zero price today, but a nonnegative value tomorrow in all circumstances.