@要求加分@美国金融分析师面试题目－入外国投资大行必备

eeyale

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Partial list of Quant interview questions:

1. You have two glass balls and a 100-story building. You would like to
determine the lowest floor from which a glass ball will break when dropped.
What is the strategy that will minimize the worst case scenario for number of
drops? What is your strategy if you have 100 glass balls?

2. A rabbit sits at the bottom of a staircase with n stairs. The rabbit can
hop up only one or two stairs at a time. How many different ways are there for

the rabbit to ascend to the top of the stairs?

3. A drunken man is on a 100 meter long bridge at the 17 meter position. He
has a 50% chance of staggering forward and backward one meter per step. What
is the probability he will make it to the end of the bridge before the
beginning?

4. Assume zero interest rate and a stock with current price $1. When the price

hits level $H for the first time you can exercise the option and will receive
$1. What is this option worth to you today?

5. A family has two children. If one of them is a boy, what is the probability
the other child is a boy?

6. You start with one amoeba. After one minute the amoeba can die, stay the
same, split into two or split into three with equal probability. What is the
probability the amoeba population will ever die out?

7. Suppose you have a coin with probability p of tossing heads. What is the
expected number of coin tosses to get two heads in a row?

8. A banker gets off work at some random time between 6:00 pm and 7:00 pm. He
walks to the subway and takes the first of two trains that arrives. One of
these travels downtown to his mother, the other travels uptown to his
girlfriend. His mother complains that she never sees him since she has only
seen him twice in the last 20 working days. Explain this.

9. Two people arrive at the center of town at some random time between 5:00 am

and 6:00 am. They stay exactly five minutes and then leave. What is the
probability they will meet on a given day?

10. A baker sells on average 20 cakes in one day. What is the probability he
will sell an even number of cakes on any given day?

11. Airborne spores produce tiny mold colonies on gelatin plates in a
laboratory. The many plates average 3 colonies per plate. What fraction of
plates will have exactly 3 colonies?

12. You walk out of an airport, and the first bus you see has number 26 on it.

Assume buses with all numbers up to some number N exist. Estimate N.

13. Coupons in cereal boxes are numbered 1 to 5, and a set of one each is
required for a prize. With one coupon per box, how many boxes on average are
required to make a complete set?

14. Explain linear regression. What is the model? How do you estimate the
parameters? Prove this.

15. Solve the following ordinary differential equations.
y'' + y' + y = 1
y'' + 2y' + y = 1

16. Graph vega for a digital option.

17. Prove it is never optimal to exercise an American call on a non-dividend
paying stock.

18. What is the martingale measure of the forward price for a non-dividend-
paying stock?

19. Describe a function for which using antithetic variables in a Monte Carlo
simulation produces no advantage.

20. Suppose you have two random variables, one uniformly distributed on inter-

val [3; 3] and the other standard normal. Is it possible for them to have
correlation 1 or -1? What if the first variable is T-distributed?

21. What is the price of a swap? Choose the swap rate so the initial price is
zero. Let V_t be the price of the swap. You would like to model V_t using
Brownian motion. Would this work? Why or why not?

22. Derive Newton's method for finding the zero of a function.

23. Define Brownian Motion. Suppose W~N(0; 1) and t measures time. Is the
random variable Sqrt(t)*W Brownian Motion?

24. Use a binomial tree to price a call option with strike K. Assume zero
interest rate. Use parameters
S0 = 18
Su = 22
Sd = 16
K = 19.

25. Design a C++ routine that will efficiently compute exp(x) to n terms.

26. Design a class or classes in C++ that will model a deck of cards.

27. Which pricing measure is most relevant for pricing credit derivatives,
risk- neutral or physical? Why?

28. Give an example where Value at Risk is not subadditive.

29. Describe a situation where Value at Risk is always subadditive.

30. Suppose you have a string that is one unit long, and you cut it in two
places uniformly distributed. What is the probability you can make a triangle
out of the three pieces? If you instead make the second cut on the longest
piece, what is then the probability you can make a triangle out of the pieces?


31. Define standard Brownian motion. Compute P(W1 > 0;W2 < 0), where W1
and W2 are standard Brownian motion at times 1 and 2.

32. Prove that standard Brownian motion hits a level with probability 1. Is
this also true in higher dimensions?

33. What is the distribution of the minimum of a Brownian motion? How about
a Brownian motion plus a Poisson process?

34. How would you price a swaption today when the swap begins today?

35. How would you price a swaption today when the swap begins in one month?

36. What is a Eurodollar future?

37. What is a swaption?

38. What is smile and skew? How do you model them?

39. What is the advantage of HJM over regular affine models? Can you fit the
initial term structure for any affine models?

40. Draw on one graph the Black Scholes price of a call option as a function
of the stock price for two option, one with maturity 1 and the other with
maturity 2.

[此贴子已经被作者于2006-3-7 14:15:54编辑过]