Brainteaser: Math

Round 1: Investment Bank Quantitative Research

Question: An ant is placed on one vertex of a unit cube. What is the shortest path the ant can take to get to the opposite vertex (walking on the surface of the cube, it cannot fly)?

Financial Derivatives: Options

Round 2: Investment Bank Quantitative Research

Question 1: What are the assumptions of Black-Scholes model?

Question 2: What is Implied Volatility?

Question 3: If you want to replicate (approximately) a digital call option using vanilla calls and puts, how do you do it?

Financial Derivatives: Bonds

Round 1: Investment Bank Quantitative Research

Question 1: What is duration (of a bond)?

Question 2: Rank the following four (4) bonds in order of their duration (or state what’s ambiguous otherwise):

6% coupon, 3 year
5.5% coupon, 3 year
3-year zero coupon
2-year zero coupon

Numerical Methods: Monte Carlo

Round 2: Investment Bank Quantitative Research

Question 1: In Monte Carlo simulation, name a few ways to reduce variance.

Question 2: Give an example (in finance) where you would use control variates?

Programming: C++

Round 1: Investment Bank Quantitative Research

Question 1: In the following function header: const int foo(const Bar & b) const; , what is each const for?

Question 2: Is there a way to avoid or circumvent the behaviour of the last const above?

Question 3: In the following statement: const char * const p = q;, what is each const for?

Brainteaser: Probability

Round 1: Hedge Fund Quantitative Research

Question: You have a deck of black and red cards (you know the number of cards for each color). You draw cards one by one. You can stop any time you want. If you guess the color of next card correctly, you win 1 dollar. Cards are not returned to the deck after being drawn. What is the optimal stopping rule in terms of maximizing expected payoff? Also, what is the expected payoff following this optimal rule?