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cycinter · 2024年02月15日

为什么delta是30000,为什么是用delta normal

NO.PZ2018122701000048

问题如下:

A portfolio manager owns a portfolio of options on a non-dividend paying stock RTX. The portfolio is made up of 10,000 deep in-the-money call options on RTX and 50,000 deep out-of-the money call options on RTX. The portfolio also contains 20,000 forward contracts on RTX. RTX is trading at USD 100. If the volatility of RTX is 30% per-year, which of the following amounts would be closest to the 1-day VaR of the portfolio at the 95 percent confidence level, assuming 252 trading days in a year?

选项:

A.

USD 932

B.

USD 93,263

C.

USD 111,122

D.

USD 131,892

解释:

B is correct.

考点 Mapping to Option Position

解析 We need to map the portfolio to a position in the underlying stock RTX. A deep in-the-money call has a delta of approximately 1, a deep out-of-the-money call has delta of approximately 0 and forwards have a delta of 1. The net portfolio has a delta of about 30,000 and is approximately gamma neutral. The 1-day VaR estimate at 95 percent confidence level is computed as follows:

α×S××σ×SQRT(1/T)=1.645×100×30000×0.3×SQRT(1/252)=93263

为什么delta是30000,为什么是用delta normal,没懂

1 个答案

pzqa39 · 2024年02月15日

嗨,努力学习的PZer你好:


deep in-the-money call options每份合约的delta是1,有10000份合约;forward contracts每份合约的delta是1,有20000份合约,加起来是30000份delta为1的合约。而deep out-of-the money call options每份合约的delta为0,所以整个组合相当于是30000*1+50000*0=30000。


delta-normal是求VaR的一种方法,这道题考察的是公式VaR(dc) = |delta| * VaR(ds) ,VaR(ds)=区间调整*σ*日期调整*股票价格,把数代入公式计算即可。

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