So I just finished the above interview for a sophmore internship position. The questions I got were as follows:
Describe the difference between a forward rate agreement and a eurodollar future
Take the derivative of this equation: x+...+x=? (x times) What does this equal and where is the problem?
State Ito's Lemma
State Jensen's Inequality
then numerous other easier questions. Is this surprising for a sophomore interview or was I just ill prepared?
depends on your background. math and probability
"Describe the difference between a forward rate agreement and a eurodollar future
Take the derivative of this equation: x+...+x=? (x times) What does this equal and where is the problem?
State Ito's Lemma
State Jensen's Inequality"
first one is actually quite tricky, depending on what level of depth they want.
second is not hard at all, if you have a math background at all this is really fair game. this is by far the easiest of the bunch
three and four are definitions you should know if you have a math/probability background.
yeah but as a sophomore? I am taking stochastic this semester and both those definitions are covered. I thought I was really advanced to be taking stochastic as a sophomore but I guess not. the answers were as follows
1: their rho's are different because of the difference in frequency of adjustment of the price to current interest rates.
2: x+ ... +x =x^2 d/dx = 2x=x. problem is the differentiation because of the first sum is only true for integers and not rationals, so its a step function and thus discontinuous and not differentiable.
3: df(x(t),t)=(df/df+a(t,w)df/dx+1/2b(t,w)^2d^2f/dx^2)dt + b(t,w)df/dxdWt
4:phi(sum(ax)/sum(a)) leq sum(phi(x))/n
yeah but as a sophomore? I am taking stochastic this semester and both those definitions are covered. I thought I was really advanced to be taking stochastic as a sophomore but I guess not. the answers were as follows
1: their rho's are different because of the difference in frequency of adjustment of the price to current interest rates.
2: x+ ... +x =x^2 d/dx = 2x=x. problem is the differentiation because of the first sum is only true for integers and not rationals, so its a step function and thus discontinuous and not differentiable.
3: df(x(t),t)=(df/df+a(t,w)df/dx+1/2b(t,w)^2d^2f/dx^2)dt + b(t,w)df/dxdWt
4:phi(sum(ax)/sum(a)) leq sum(phi(x))/n
State the importance of Ito's Lemma and Jensen's Inequality. That's a much better question than seeing if you've memorized a formula.
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