GS equity derivatives trader interview

For number 3 would it just be 3.5? It seems like there is no difference whether you have three rolls or a million if you are only paid based on the last one.

ActuarialQuant

My guess (take with a grain of salt here) would probably be along the lines of brainteasers, EV/probability (think coin, dice, gambling setting), option payoff (know your Greeks intuitively!), potentially a coding aspect at some point, and maybe your general pulse on the market. Here's a typical sample platter I might ask personally: 

1. You're outside a room with 3 light switches, each controlling one of the light bulbs. If you can only enter the room once, how can you determine which switch controls which light bulb?

2. You have two decks of cards: 13 reds & 13 blacks. The other has 26 reds & 26 blacks. We play a game in which you select one of the two decks and pick two cards from it - you win the game if you select two black cards. Which deck should you pick to maximize your chances of winning?

3. You can roll a dice up to 3 times. You are going to be paid by the face value of your last roll. How much are you willing to pay?

4. How would you use a Monte Carlo simulation to compute pi?

5. What is a strangle? If you don't know, I'll probably define it for you, give you some reference points and then ask if with the given info, can you draw me what the payoff graph looks like?

6. If you're long puts, what are your net positions for these greeks: delta, gamma, theta, vega. What if you're only short the underlying contract? 

7. I might ask you what the last quote you saw for the DJI was, maybe pick your thoughts on where you see oil headed, etc. 

8. Probably not asked as much these days, but for shits & giggles I'd see how fast you can do something like 57*43 in your head. 

Remember, you don't have to always get the right answer. It's more about your overall thought process and how well you respond under stress.  

Great questions! Would you mind sharing the answers

1. Wall Street interview book

2. P(2 blacks from deck 1)=13/26*12/25, P(2 blacks from deck2)=26/52*25/51, deck 2 gives the maximum winning chance

3. 1st roll:text book answer: (1+2+3+4+5+6)/6=6*7/2/6=3.5, 2nd roll: 3.5*1/2+1/6(4+5+6)=4.25, 3rd roll: 4.25*4/6+1/6(5+6)=4.6667, n roll: converging to 6 infinitely

the correct strategy is that if first roll is less than 3, roll again, if 2nd roll is bigger than 3, stop, if 2nd roll is smaller than 3, roll for the 3rd time

4.

counter=0

for i in range(n): 

         X=2*Unif(0,1)-1, Y=2*Unif(0,1)-1

         if X^+Y^2<=1: counter+=1

pi=4*counter/n

5. long strangle: ATM straddle with bigger gap in the middle 

6. long puts: delta negative or 0, gamma always positive, theta always negative , vega always positive. short U.D: negative delta=1

7.

8.57*43=50*50-7*7=2451