SOCR EduMaterials Activities ApplicationsActivities StockSimulation
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(Difference between revisions)
(New page: == A Model for Stock prices == * '''Description''': You can access the stock simulation applet at http://www.socr.ucla.edu/htmls/app/ . * Process for Stock Prices: Assumed a drift rate...) |
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\frac{\Delta S}{S}=0.14 \Delta t + 0.20 \epsilon \sqrt{\Delta t} | \frac{\Delta S}{S}=0.14 \Delta t + 0.20 \epsilon \sqrt{\Delta t} | ||
</math> | </math> | ||
- | * Find the distribution of the change in <math>S<math> divided by <math>S<math> at the end of the first year. That is, find the distribution of <math>\frac{\Delta S}{S}</math>. <br> | + | * Find the distribution of the change in <math>S</math> divided by <math>S</math> at the end of the first year. That is, find the distribution of <math>\frac{\Delta S}{S}</math>. <br> |
<math> | <math> | ||
\frac{\Delta S}{S} \sim N\left(0.10 \Delta t, 0.20 \sqrt{\Delta t}\right). | \frac{\Delta S}{S} \sim N\left(0.10 \Delta t, 0.20 \sqrt{\Delta t}\right). | ||
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\Delta S_1 = S_0 + \Delta S_1 = 20 + 0.26=20.26. | \Delta S_1 = S_0 + \Delta S_1 = 20 + 0.26=20.26. | ||
</math> | </math> | ||
- | We continue in the same fashion until we reach the end of the year. | + | We continue in the same fashion until we reach the end of the year. Here is the SOCR applet. |
<center>[[Image: Christou_stock_simulation.jpg|600px]]</center> | <center>[[Image: Christou_stock_simulation.jpg|600px]]</center> |
Revision as of 16:08, 3 August 2008
A Model for Stock prices
- Description: You can access the stock simulation applet at http://www.socr.ucla.edu/htmls/app/ .
- Process for Stock Prices: Assumed a drift rate equal to μS where μ is the expected return of the stock, and variance σ^{2}S^{2} where σ^{2} is the variance of the return of the stock. From Weiner process the model for stock prices is:
or
Therefore
S Price of the stock.
ΔS Change in the stock price.
Δt Small interval of time.
ε Follows N(0,1).
- Example: The current price of a stock is . The expected return is μ = 0.10 per year, and the standard deviation of the return is σ = 0.20 (also per year).
- Find an expression for the process of the stock.
- Find the distribution of the change in S divided by S at the end of the first year. That is, find the distribution of .
- Divide the year in weekly intervals and find the distribution of at the end of each weekly interval.
- Therefore, sampling from this distribution we can simulate the path of the stock. The price of the stock at the end of the first interval will be S_{1} = S_{0} + ΔS_{1}, where ΔS_{1} is the change during the first time interval, etc.
- Using the SOCR applet we will simulate the stock's path by dividing one year into small intervals each one of length of a year, when .
- The applet will select a random sample of 100 observations from N(0,1) and will compute
Suppose that ε_{1} = 0.58. Then
Therefore
ΔS_{1} = S_{0} + ΔS_{1} = 20 + 0.26 = 20.26.
We continue in the same fashion until we reach the end of the year. Here is the SOCR applet.