An Intuition-Based Options Primer for FE
Ideal for entry level positions interviews and graduate studies, specializing in options trading arbitrage and options valuation models.
\(f(x) = x^3-x+1=0\)
\(f'(x)=3x^2-1=0\)
\(x_1=\frac{1}{sqrt(3)} x_2=-\frac{1}{sqrt(3)}\)
\(f(\frac{1}{sqrt(3)}) = 0.615100\) - minimum
\(f(-\frac{1}{sqrt(3)}) = 1.384900\) - maximum
\(f(-infinity) = -infinity\) it means you have a solution for f(x)=0
such solution is close to
x = -1.3247179574971
with approximation error = .0000000010761969093664
\(f(x) = x^3-x+1=0\)
\(f'(x)=3x^2-1=0\)
\(x_1=\frac{1}{sqrt(3)} x_2=-\frac{1}{sqrt(3)}\)
\(f(\frac{1}{sqrt(3)}) = 0.615100\) - minimum
\(f(-\frac{1}{sqrt(3)}) = 1.384900\) - maximum
\(f(-infinity) = -infinity\) it means you have a solution for f(x)=0
such solution is close to
x = -1.3247179574971
with approximation error = .0000000010761969093664
The question did not ask to find the root. I put this question here because I did exactly the same like your answer plus Vadim's answer.
My lecturer raised a good question: Do you need to answer what I do not ask for?
The main issue is understanding of the question. So, do we really understand the market when we do maths or modeling??
I leave it to you. What the question is actually ask for is more important in this aspect. I did not ask to find the root.
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