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leeciyuan · 2018年11月07日

这题怎么做呀

A stock is trading USD 100. A box spread with 1 year to expiration and strikes at USD 120 and USD 150 is trading at USD 20. The price of a 1-year European call option with strike USD 120 is USD 5 and the price of a European put option with same strike and expiration is USD 25. What strategy exploits an arbitrage, if any?

a. Short (1) put, short (1) unit of spot, buy one call, and buy six unit box-spread

b. Buy (1) put, short (1) unit of spot, short (1) call, buy (4) units of box-spread

c. Buy (1) put, buy (1) unit of spot, short (1) call, and short (6) units of box-spread

d. There are no arbitrage opportunities


没听懂做题过程,可以详细写一下吗?还有网上这题是选A?

1 个答案

orange品职答疑助手 · 2018年11月07日

同学你好,首先不好意思,你说的没错,这道题应该选A。之前也有同学反映过这道题,我们的勘误是定期的,会尽快地把勘误给到大家。


这边其实和box spreads关系不大,主要的是put-call-parity内,可以进行套利:通过put-call-parity,我们发现:short put, short S, long call的现金流为25+100-5=120=K*e^(-RT),而K是等于120的,所以实际的行权价是偏低的。
因此,我们short put, short S, long call得到120的现金后,现在去买box spread。在T时刻,box spread带来120*(1+Rf)的钱,然后以120行使看涨期权,买回S、还掉现货,从而实现套利

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