WEEK 3 QUIZ 10/10 GRADE!

Question 1Letf(x,y)=sin(xy). Computefx.Answer for Question 1You entered:PreviewHelpYour AnswerScoreExplanation

y*cos(x*y)Correct1.00

Total1.00 / 1.00

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To compute the partial derivative wrtx, treatyas a constant and take the derivative offas a function of a single variablex.Question 2Letf(x,y)=sin(xy). Compute2fxy.Answer for Question 2You entered:PreviewHelpYour AnswerScoreExplanation

cos(x*y)-(y*x*sin(x*y))Correct1.00

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Take the partial derivative offwrtythen take the partial derivative offywrtx.Question 3Compute the Hessian of the functionf(x,y)=sin(xy)and evaluate it at the point(,). How many unique values are there?Your AnswerScoreExplanation

1

2Correct1.00

3

4

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The Hessian is the array of second order partial derivatives.Question 4Letf(x,y)=x2+y2,x=sin(), andy=cos(). Computedfd.Answer for Question 4You entered:PreviewHelpYour AnswerScoreExplanation

0Correct1.00

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Short cut: substitutex=sin()andy=cos()into the expression forfto see thatf(x,y)=1. Make sure you understand the chain rule formula though. (please provide answer as a numerical response.)Question 5LetF(x,y)=cos(x)sin(y)14=0. Computedydx.Answer for Question 5You entered:PreviewHelpYour AnswerScoreExplanation

tan(x)*tan(y)Correct1.00

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Use implicit differentiation.Question 6vega(P)=vega(C)Your AnswerScoreExplanation

TrueCorrect1.00

False

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Take the partial derivative of the put-call parity relation wrt.Question 7Does an increase inShave a positive or negative effect on the price of a European call option?Your AnswerScoreExplanation

PositiveCorrect1.00

Negative

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Is(C)greater than or less than zero?Question 8Does an increase inShave a positive or negative effect on the Delta()of a European call option?Your AnswerScoreExplanation

PositiveCorrect1.00

Negative

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Isgreater than or less than zero?Question 9Does a positive change inrhave a positive or negative effect on the price of a European call option?Your AnswerScoreExplanation

PositiveCorrect1.00

Negative

Total1.00 / 1.00

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Isgreater than or less than zero?Question 10Does a positive change inthave 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., thatq=0)?Your AnswerScoreExplanation

Positive

NegativeCorrect1.00

Total1.00 / 1.00

Question Explanation

Isgreater than or less than zero?