Linearization

[Guest]

Hello!

Considering the equation in the file, I need to linearize the right hand side in a way that all the components, including the ones inside the exponential are independent of each other, or to prove that the conclusions of a certain linear equation in which these components are all independents are the same as the results of the equation above (e.g. the higher M, the more S_1 approaches S_1*exp(E_1[r]T) and b_1 tends to zero).


Thank You!

[Guest]

The simplest way to "linearize" any function about a given value of x is to write that function as a power seriex (Taylor's series) about that point then drop all terms with exponent 2 or higher. Of course, this is equivalent to replacing the function with the tangent line to the graph and, again, that depends upon the x value at which you are "linearizing".