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台风来了 · 2023年08月16日

如何计算模拟的期权的各组成部分的具体金额?

NO.PZ2023041003000034

问题如下:

Messer explains, “Of course, with the index moving down 10% in the last twelve months, the payoffs with these options could have been replicated without using options.” Szillat responds, “My understanding is that the payoff would have been the same as the call option if you had purchased 0.5697 index units and lent EUR 356.79 at the 1-year interest rate.”

With respect to his assessment of replicating the option payoff, Szillat is least likely correct about:

选项:

A.

lending EUR 356.79.

B.

using the one-year interest rate.

C.

purchasing 0.5697 index units.

解释:

Szillat is incorrect in his method of replicating the call option. It can be replicated by purchasing the amount of the underlying shares designated by the hedge ratio and then borrowing (not lending) an amount equal to the present value of ((hedge ratio × S–) + c–).

老师,您好!


答案解析中:It can be replicated by purchasing the amount of the underlying shares designated by the hedge ratio and then borrowing (not lending) an amount equal to the present value of ((hedge ratio × S–) + c–). 从put-call parity公式可以知道大概如何模拟put或call option。但是如何计算股票和债券具体金额多少呢?麻烦补充一下,谢谢!

1 个答案

Lucky_品职助教 · 2023年08月17日

嗨,从没放弃的小努力你好:


套期保值比率(hedge ratio)是衡量期权价格变化对基础资产价格变化的敏感性。它通常是基于期权价格和基础资产价格的历史波动率来计算的。一旦确定了套期保值比率,可以使用以下步骤来模拟一个看涨期权的套期保值策略:

  1. 购买股票:首先,计算出需要购买多少股票,这是根据套期保值比率和期权合约中表示的股票数量来确定的。假设套期保值比率为0.5697,如果期权合约表示每个合约等于1单位的股票,那么需要购买0.5697单位的股票。
  2. 借款:接下来,需要借款来购买这些股票。借款的数量应该等于套期保值策略所需的资金,这是由套期保值比率、股票价格和期权价格共同决定的。具体计算是根据套期保值比率乘以(S - c),其中S是股票价格,c是期权价格。这个数量代表了购买股票所需的金额。
  3. 借款利率:还需要考虑借款的利率,因为需要偿还借款。借款的数量等于套期保值比率乘以(S - c),而不是Szillat提到的EUR 356.79。


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