NO.PZ2020021203000072
问题如下：
A four-month European call option on a stock is currently selling for USD 2.50. The current stock price is USD 54, and the strike price is USD 50. A dividend of USD 1.50 is expected in one month. The risk-free interest rate is 3% per annum (annually compounded) for all maturities. What opportunities are there for an arbitrageur?
选项：
解释：
The lower bound for the option price is
The option is selling for less than its lower bound. An arbitrageur can buy the option and short the stock for an initial cash inflow of USD 51.50. The arbitrageur has to pay dividends of USD 1.50 after one month.
If the option is exercised, the cost of closing out the short position will be USO 50. If it is not exercised, the cost of closing out the short position will be less than USD 50. The worst-case scenario for the arbitrageur is therefore:
Today: +51.50,
One month: -1.50, and
Four months: -50.00.
When the discount rate is zero, the sum of these cash flows will have zero present value. Any positive discount rate gives a positive sum of present values.
When the discount rate is zero, the sum of these cash flows will have zero present value. Any positive discount rate gives a positive sum of present values.麻烦讲解下这几句，谢谢
