NO.PZ202208260100000802
问题如下:
If Kleinert's clients observe that the one-year put option with a €100 exercise price is trading at €2.50, which of the following statements best describes how Kleinert's clients could take advantage of this to earn a risk-free return greater than 0.37% over the year.
选项:
A.Kleinert should purchase the put option and also purchase approximately 0.23 shares per option to match the hedge ratio.
B.Kleinert should purchase the put option and purchase 50% of the underlying shares given the 50-50 chance the stock will fall and the put option exercised.
C.Kleinert should purchase the put option and purchase 47% of the underlying shares to match the risk-neutral probability of put exercise.
解释:
Solution
A is correct.
If the put option can be purchased for less than the no-arbitrage price, then a potential arbitrage opportunity is available. In this case, Kleinert's clients should purchase the underpriced put option and buy h* units of SparCoin's stock. The hedge ratio, h*, is calculated as:
Note that the negative hedge ratio implies that both the put option and underlying are purchased or sold to create a hedge. This initial purchase of the put option and stock will cost:
€2.50 + 0.2276 × €105.25 = €26.45.Should the stock price decrease, the value of this portfolio will be:
The strategy generates a risk-free return of (€26.83 – €26.45)/€26.45 = 1.44%, which is greater than the 0.37% return on other available risk-free investments.
中文解析
由上面一问我们可以知道,该看跌期权的无套利价格是2.78,现在市场上看跌期权的价格是2.50。根据低买高卖的套利原理,我们应该买入该看跌期权,对应的如果构成hedged
portfolio,需要long stock。然后根据公式计算h为0.2276份。
此时,一份的put和0.2276份stock可以构成一个hedged portfolio.
该组合初始价值为:€2.50 + 0.2276 × €105.25 = €26.45
计算当股价下跌的时候,组合新的价值V1为€26.83.
此时可以计算得到return为1.44%,是大于题干所说的高于0.37%的。
当然,就选出答案来说,只需计算出h即可。
麻烦解释一下这题。。