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Warning: The hard deadline has passed. You can attempt it, but you will not get credit for it. You are welcome to try it as a learning exercise.

Quiz 3: There is one question for each of the 10 topics from week 3. The time limit is 1 hour and you only get one try so make sure you have your notes and the week 3 slides handy. Good luck!

Question 1

Let f(x,y)=sin(xy). Compute ∂f∂x.
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Question 2

Let f(x,y)=sin(xy). Compute ∂2f∂x∂y.
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Question 3

Compute the Hessian of the function f(x,y)=sin(xy) and evaluate it at the point (π√,π√). How many unique values are there?

Question 4

Let f(x,y)=x2+y2, x=sin(θ), and y=cos(θ). Compute dfdθ.
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Question 5

Let F(x,y)=cos(x)sin(y)−14=0. Compute dydx.
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Question 6

vega(P)=vega(C)

Question 7

Does an increase in S have a positive or negative effect on the price of a European call option?

Question 8

Does an increase in S have a positive or negative effect on the Delta (Δ) of a European call option?

Question 9

Does a positive change in r have a positive or negative effect on the price of a European call option?

Question 10

Does a positive change in t have a positive or negative effect on the price of a European call option (assume that the underlying asset does not pay a dividend, i.e., that q=0)?
    
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