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xyrg+ · 2023年04月20日

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  1. FRM I
  2. Financial Markets And Products

NO.PZ2016082404000030

问题如下：

A bank has sold USD 300,000 of call options on 100,000 equities. The equities trade at 50, the option strike price is 49, the maturity is in three months, volatility is 20%, and the interest rate is 5%. How does the bank delta-hedge?

选项：

A.

  Buy 65,000 shares

B.

  Buy 100,000 shares

C.

  Buy 21,000 shares

D.

  Sell 100,000 shares

解释：

ANSWER: A

This is an at-the-money option with a delta of about 0.5. Since the bank sold calls, it needs to delta-hedge by buying the shares. With a delta of 0.5, it would need to buy approximately 50,000 shares. Answer A is the closest. Note that most other information is superfluous.

“这个意思就是我们需要买入call option标的物的股票数量的50%来进行对冲，也就是100000股股票的50%，等于买入50000股股票。”

怎么理解这句话?Δ的含义不是ΔC/ΔP，是P变动对C的影响。那怎么能用Δ=多少确定对冲数量呢？

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1 个答案

李坏_品职助教 · 2023年04月21日

嗨，爱思考的PZer你好：


delta的含义是股票如果变动1%，那么期权价格变动delta%。

所以股票价格变动：期权价格变动 = 1：delta。为了用股票对冲期权价格风险，股票数量：期权数量应该是delta : 1。也就是每1份期权要用delta只股票对冲风险。

现在期权一共有30万个，一共对应10万股，所以需要delta * 10万股股票来对冲风险。


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