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Parameters Estimation in ABM
Suppose you have historical price data and you want to use Arithmetic Brownian motion model. How are you going to get the parameters of drift m and volatility s?
Recall
ABM model is
The idea of two-steps process parameter estimation for linear model is using the
analogy of finding points to determine a line. Suppose we want to find a line
equation
Step
1. Using similar idea, we can first assume the volatility is equal to zero and
we use simple regression model to fit the data with the model
Step
2. In the second step, we use the parameter
The parameter
For our examples, we generate a simulated data using set of parameters drift
Figure below show two representations of our examples with the true parameters that generate the data and their estimations. Notice that the model is always a straight line of the trend. The boundary is larger over time to show that the accuracy of prediction is lower by longer time from now.
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These tutorial is copyrighted .
Preferable reference for this tutorial is
Teknomo, Kardi. (2017) Stochastic Process Tutorial .
http://people.revoledu.com/kardi/tutorial/StochasticProcess/