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JK_MMMM · 2022年04月14日

如果u不等于0, dt怎么求？

  1. FRM I
  2. Quantitative

NO.PZ2016062402000027

问题如下：

Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift μ = 0, volatility σ = 0.14, and time step Δ = 0.01. Let StS_t be the price of the stock at time t. If S0S_0 = 100, and the first two simulated (randomly selected) standard normal variables are ε1\varepsilon_1 = 0.263 and ε2\varepsilon_2 = -0.475, what is the simulated stock price after the second step?

选项：

A.

96.79

B.

99.79

C.

99.97

D.

99.70

解释：

The process for the stock prices has mean of zero and volatility of σ△t=0.14×0.01=0.014\sigma\sqrt{\bigtriangleup t}=0.14\times\sqrt{0.01}=0.014, Hence the first step is S1=S0(1+0.014×0.263)=100.37S_1=S_0{(1+0.014\times0.263)}=100.37. The second step is S2=S1(1+0.014×−0.475)=99.70S_2=S_1{(1+0.014\times-0.475)}=99.70

老师您好，


如果u不等于0，dt怎么求？


dSt = u*S*dt+Stadndard deviation * St*dz



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DD仔_品职助教 · 2022年04月14日

嗨，爱思考的PZer你好：


dt就是delta t，只不过在微分里我们把delta写成d，dt就是time step也就是题目给出来的0.01。

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NO.PZ2016062402000027问题如下 Suppose you simulate the pripath of stoHHF using a geometric Brownimotion mol with ift μ = 0, volatility σ = 0.14, antime step Δ = 0.01. Let StS_tSt​ the priof the stotime t. If S0S_0S0​ = 100, anthe first two simulate(ranmly selecte stanrnormvariables are ε1\varepsilon_1ε1​ = 0.263 anε2\varepsilon_2ε2​ = -0.475, whis the simulatestopriafter the seconstep?96.79 99.79 99.97 99.70 The process for the stoprices hmeof zero anvolatility of σ△t=0.14×0.01=0.014\sigma\sqrt{\bigtriangleup t}=0.14\times\sqrt{0.01}=0.014σ△t​=0.14×0.01​=0.014, Henthe first step is S1=S0(1+0.014×0.263)=100.37S_1=S_0{(1+0.014\times0.263)}=100.37S1​=S0​(1+0.014×0.263)=100.37. The seconstep is S2=S1(1+0.014×−0.475)=99.70S_2=S_1{(1+0.014\times-0.475)}=99.70S2​=S1​(1+0.014×−0.475)=99.70请问这道题是哪个知识点

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