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Q1.

The gradient of a smooth function is

Answer: A
Q2.

The Newton-Raphson method

Answer: B
Q3.

What is a Hessian?

Answer: C
Q4.

The bisection method can be used for solving f(x)=0 for a unique solution of x, when

Answer: A
Q5.

When calculating the implied volatility from an option price we use the bisection method and know initially that the volatility is somewhere between 1% and 100%. How many iterations do we need in order to determine the implied volatility with accuracy of 0.1%?

Answer: A

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