题目
A 1-year forward contract on a stock with a forward price of USD 100 is available for USD 1.50. The table below lists the prices of some barrier option on the same stock with a maturity of 1 year and strike of USD 100. Assuming a continuously compounded risk-free rate of 5% per year what is the price of a European put option on the stock with a strike of USD 100.「huixue_img/importSubject/1564169527904833536.png」
选项
A.USD 2.00
B.USD 4.90
C.USD 5.11
D.USD 6.61
答案
C
解析
●The sum of the price of up-and-in barrier call and up-and-out barrier call is the price of an otherwise the same European call. The price of the European call is therefore USD5.21+USD1.40=USD6.61. ●The Put-Call parity relation gives Call - put = Forward (with same strikes and maturities) ●Thus, 6.61-put=1.50. Thus put=6.61-1.50=5.11.障碍期权有一个特点，叫做敲入-敲出平价（In-out parity）。指的是如果把一个同样障碍价格敲入期权和一个同样障碍价格的敲出期权结合在一起，就可以构造出一个普通的期权。因此，上涨-敲入式看涨期权和上涨-敲出式看涨期权就可以构造出一个普通的看涨期权。然后根据买卖权评价公式求解欧式看跌期权价格。