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梦梦 · 2024年11月11日

contract value is 10/index 是什么意思？

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2023091701000092

问题如下：

An at-the-money European call option on the DJ EURO STOXX 50 index with a strike of 2200 and maturing in 1 year is trading at EUR 350, where contract value is determined by EUR 10 per index point. The risk-free rate is 3% per year, and the daily volatility of the index is 2.05%. If we assume that the expected return on the DJ EURO STOXX 50 is 0%, the 99% 1-day VaR of a short position on a single call option calculated using the delta-normal approach is closest to:

选项：

A.EUR 8

B.EUR 53

C.EUR 84

D.EUR 525

解释：

Since the option is at-the-money, the delta is close to 0.5. Therefore a 1 point change in the index would translate to approximately 0.5 × EUR 10 = EUR 5 change in the call value. Therefore, the percent delta, also known as the local delta, defined as %D = (5/350) / (1/2200) = 31.4.

So the 99% VaR of the call option = %D × VaR(99% of index) = %D × call price × alpha (99%) × 1-day volatility = 31.4 × EUR 350 × 2.33 × 2.05% = EUR 525. The term alpha (99%) denotes the 99th percentile of a standard normal distribution, which equals 2.33.

There is a second way to compute the VaR. If we just use a conversion factor of EUR 10 on the index, then we can use the standard delta, instead of the percent delta:

VaR(99% of Call) = D × index price × conversion × alpha (99%) × 1-day volatility = 0.5 × 2200 × 10 × 2.33 × 2.05% = EUR 525, with some slight difference in rounding.

Both methods yield the same result.

with a strike of 2200，这里是点，不是金额对吧？

contract value is 10/index，合约价值是一点10元，合约价值是什么意思？和学期权时的payoff=max（0，S-X）是一个意思吗？

我看执行价格直接用2200乘以10了，是啥原理呢


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2 个答案

pzqa27 · 2024年11月14日

嗨，从没放弃的小努力你好：


执行价是用于判断是否行权的，比如这个2200，如果index点数高于2200了，那就执行call，但是具体执行交易的时候总不能拿点数去买index吧，所以这里给了一个乘数，就是按每点10元来进行交易。

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pzqa27 · 2024年11月12日

嗨，努力学习的PZer你好：


with a strike of 2200，这里是点，不是金额对吧？

嗯，是的。


contract value is 10/index，合约价值是一点10元，合约价值是什么意思？和学期权时的payoff=max（0，S-X）是一个意思吗？

这里2200是点位，但是具体交割要花多少钱没说，所以这里给了1点值10块，一共2200点，所以是2200*10

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梦梦 · 2024年11月13日

我的意思是执行价格和合约价格有啥关系，为啥执行价格的点数乘以合约的每点金额

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NO.PZ2023091701000092 问题如下 at-the-money Europecall option on the EUROSTOXX 50 inx with a strike of 2200 anmaturing in 1 yeis trang EUR350, where contravalue is termineEUR 10 per inx point. Therisk-free rate is 3% per year, anthe ily volatility of the inx is 2.05%.If we assume ththe expectereturn on the EURO STOXX 50 is 0%, the 99%1-y Vof a short position on a single call option calculateusing thelta-normapproais closest to: A.EUR 8 B.EUR 53 C.EUR 84 EUR 525 Sinthe option isat-the-money, the lta is close to 0.5. Therefore a 1 point change in theinx woultranslate to approximately 0.5 × EUR 10 = EUR 5 change in the callvalue. Therefore, the percent ltalso known the locltfineas%= (5/350) / (1/2200) = 31.4. So the 99% Vof thecall option = %× VaR(99% of inx) = %× call pri× alpha (99%) × 1-yvolatility = 31.4 × EUR 350 × 2.33 × 2.05% = EUR 525. The term alpha (99%)notes the 99th percentile of a stanrnormstribution, whiequals2.33. There is a seconwayto compute the VaR. If we just use a conversion factor of EUR 10 on the inx,then we cuse the stanrltinsteof the percent ltVaR(99% of Call) = inx pri× conversion × alpha (99%) × 1-y volatility = 0.5 × 2200 × 10 ×2.33 × 2.05% = EUR 525, with some slight fferenin rounng. Both metho yielhe same result. 这道题我尝试用BSM mol来解可以吗=[ln (so/x)+ (u+v^/2)T/(vT^0.5) 因为题目说是 the money so=x然后说expectereturn = 0， 所以u = 0V 和T 都给了 我就算出来 =0.01025所以N() = 0.50399 = ltaVoption = |*Vinx

2024-10-27 05:42 1 · 回答

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2024-09-04 21:57 3 · 回答