NO.PZ201702190300000304
问题如下：
4.For the Alpha Company option, the positions to take advantage of the arbitrage opportunity are to write the call and:
选项：
A. short shares of Alpha stock and lend.
B. buy shares of Alpha stock and borrow.
C. short shares of Alpha stock and borrow.
解释：
B is correct.
You should sell (write) the overpriced call option and then go long (buy) the replicating portfolio for a call option. The replicating portfolio for a call option is to buy h shares of the stock and borrow the present value of (hS- - c-).
c = hS + PV(-hS- + c-).
h = (c+ - c-)/(S+ - S-) = (6 - 0)/(56 - 46) = 0.60.
For the example in this case, the value of the call option is 3.714. If the option is overpriced at, say, 4.50, you short the option and have a cash flow at Time 0 of +4.50. You buy the replicating portfolio of 0.60 shares at 50 per share (giving you a cash flow of -30) and borrow (1/1.05) x [(0.60 x 46) - 0] = (1/1.05) x 27.6 = 26.287. Your cash flow for buying the replicating portfolio is -30 + 26.287 = -3.713. Your net cash flow at Time 0 is + 4.50 - 3.713 = 0.787. Your net cash flow at Time 1 for either the up move or down move is zero. You have made an arbitrage profit of 0.787.
In tabular form, the cash flows are as follows:
