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Drink H · 2020年07月01日

问一道题:NO.PZ2016062402000039

问题如下:

Continuing with the previous question, you have implemented the simulation process discussed earlier using a time interval △t= 0.001, and you are analyzing the following stock price path generated by your implementation.

Give this sample, which of the following simulation steps most likely contains an error?

选项:

A.

Calculation to update the stock price

B.

Generation of random sample value for ε

C.

Calculation of the change in stock price during each period

D.

None of the above

解释:

The random variable e should have a standard normal distribution, which means that it should have negative as well as positive values, which should average close to zero. This is not the case here. This is probably a uniform variable instead.

“C的意思是通过每期服从标准正态分布的ε乘以波动率求的每期△S,波动性这个条件在上一题给的条件里应该有,或者不看上一题,就看每期△S和ε比例都相等也可以推出每期△S计算式正确的。”----ε乘以波动率求每期ΔS,这是哪里的知识点?GSM的维纳过程不是ε乘以根号Δt吗?

2 个答案

品职答疑小助手雍 · 2020年07月03日

这个要结合题干的每期递推的公式来看,就是上一问2016062402000038里的那个公式,其中分两部分,一部分是趋势项,和收益率有关就是那个0.13*△t,另一部分才是波动项也就是那个0.25*ε*根号下△t。

趋势项的存在就导致了△S和ε比例不相等

单就波动项而言比例肯定是等于0.25*根号下△t的。

品职答疑小助手雍 · 2020年07月02日

ε是服从标准正态分布的,附带上波动率才能反映波动嘛,要不它服从(0,1)的正态分布其实是和股票价格的波动不成比例的。

蒙特卡洛模拟中每期的波动量会考虑ε这个随机项、波动率和△t这三个因素。因为本题△t和波动率是固定的,所以每期的波动量肯定是和ε这个随机项成正比的啊。

这个不是哪里知识点的问题,而是你要想明白假设一个每股10万元的股票,肯定不能拿ε这个服从(0,1)标准正态分布单纯的乘以时间来计算波动量,要考虑10万这个价格的波动率的。

Drink H · 2020年07月03日

“就看每期△S和ε比例都相等”,一看就比例不等啊

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