For this example, we chose to make mu (drift) and sigma (diffusion) constants, and we chose them arbitrarily for simplicity purposes. In future videos we will go through ways to derive the constant values as well as overview when mu and sigma are continuous functions themselves. Thanks for the comment! If you have any other topics you're interested in learning about, let us know!
Upon further review, we have found an error in our labeling. You are correct, mu should be labeled as the expected return (i.e. mean), not as risk free interest rate. Thank you for your attention to detail! We look forward to hearing from you in the future!
@@chandrab For that article specifically, our goal was to build off of our "Understanding Ito Calculus" articles by showing a very basic application of a stochastic differential equation. The simplest way to do that was by keeping mu and sigma as constants. In future articles we will be incorporating more advanced techniques such as calculating mu and sigma as functions of time.
In the code, shouldn't "dt" in the formula of "X" be something like "[ n*dt for n in range(sim_steps)] "? otherwise the drift part in the exponent is just a constant, right?
Nice channel. Btw, No drift calculation?
For this example, we chose to make mu (drift) and sigma (diffusion) constants, and we chose them arbitrarily for simplicity purposes. In future videos we will go through ways to derive the constant values as well as overview when mu and sigma are continuous functions themselves. Thanks for the comment! If you have any other topics you're interested in learning about, let us know!
Upon further review, we have found an error in our labeling. You are correct, mu should be labeled as the expected return (i.e. mean), not as risk free interest rate. Thank you for your attention to detail! We look forward to hearing from you in the future!
Will you be updating the code in the medium article?
@@chandrab For that article specifically, our goal was to build off of our "Understanding Ito Calculus" articles by showing a very basic application of a stochastic differential equation. The simplest way to do that was by keeping mu and sigma as constants. In future articles we will be incorporating more advanced techniques such as calculating mu and sigma as functions of time.
Do you have anything in mind that you would like us to cover in the future?
In the code, shouldn't "dt" in the formula of "X" be something like
"[ n*dt for n in range(sim_steps)] "? otherwise the drift part in the exponent is just a constant, right?