Morgan Stanley Quant Finance 笔试
英国偶像-暑期社会实践调查报告
Morgan Stanley Quant Finance 笔试 来源：
王汉宁的日志
校内上有一篇被疯转的日志“你有去华尔街的资格么”，说的就是我标题里的这
个项目。他们的招聘现在有了笔试，今天刚笔完这个，吐血，离“去华尔街的 资
格”还有好远，权当
练习了。。90分钟100道单选，4选1，选错了扣14的分。
不让用计算器，所以碰到神马ln(2
),正态分布各种区间点这种东西 之前没记过
就无比蛋疼。如果不是知识十分全面且熟练度犹如高考，
应该很难做完吧。。。
而且据说有A,B,C,D四套题，我没看我的是哪套。几套题之间有交 叉，感
觉他
们应该是有个题库随机出的四套吧。现在把我还记得的题目（居然能回忆出一大
半！）贴出
来供大家娱乐，有些题目没看懂，有的也没记住，所以难免有
叙述
不清的情况，凑合看吧。很多不会的题各位大牛指导。
Calculus
1.
(x+2y)在平面上两条曲线间的积分,没记住
2. int(0,pi12) of
(cosx-sinx) (sinx + cosx) 还是神马的
3. Extrema of
f(x)=x^2+1x
4. Derivative of x^lnx
5.
Derivative of cos(x^2)
6. x'(t)=ax+by,
y'(t)=cx+dy, (forgot coefficients)，x(0)=4, y(0)=3,
x(1)?
(Maybe need to solve two ODEs and
determine coefficients?)
7. Fastest growing
direction of f(x)=1(1+ax^2+by^2+cz^2) at (1,1,-2)
8. int(0,inf) of exp(x^22)也可能是我看错题了是exp(-x^22)
9. Similar to the question: What is the
intersection volume of two unit
Cylinder?
Linear Algebra
1. 解二元一次方程组。。。
2. Under
which situation will a linear system has no
solutions.
3. 6 variable，3 equation，in general
how many dims do the solutions have?
1
4. (Can't remember clearly)
Positive definite matrix doesn't necessarily
have property: 1)all strict positive
diagonaleigenvalue 2)all strict
positive
diagonal of Cholesky decomposition 3)all data
positive
4)invertible
Probability &
Stat
1. Two regular coins, one fake coin with
both sides are heads. Toss one
coin u got
heads, what's that prob of tossing same coin and
getting heads
again?
2. One regular coin,
one fake coin. Pick one, toss it twice and get 2
heads.
Prob of picking the fake coin?
3.
52 poker cards => 4 piles，13 in each. 2 Aces in
one pile，the other
2 Aces in two different
piles, the rest pile doesn't have an Ace. Prob?
4. X,Y,Z have equal corr, the lower bound of
this corr? (-0.5)
5. Random variable X,Y,Z,
corr(X,Y)=corr(Y,Z)=c>0, what is the minimum
correlation between X and Z? (2c^2-1)
6.
Given data and some statistics, what is the
regression function?
7. Uniform distribution,
MLE estimator of a in U[0,a] ( (n+1)n*max(xi) )
8. 10000 coins, prob of more than 4950 heads?
(1-N(-1))
9. 100 coins, prob of more than 60
heads? (1-N(-2))
10.100 uniform variables,
...another central limit theory question
11.18
socks, 12 in one color, 6 in the other color, prob
of pick 2 to form
a pair？
g 2 from 52
poker cards, prob of a pair?
13.X have 0 mean
and 1 var, E(x+2)^2?
14.X,Y have 0 mean and 1
var, E(X|X+Y=1)? or undetermined?
in blank:
X1 X2 are iid, if for any a,b we can find c,d so
that
aX1+bX2 has same distribution of cX+d,
then the distribution is: normal,
Poisson,
stable, (forgot the last choice)
2
people (one from Harvard and one from MIT...)
arrive uniformly
between 12pm - 1pm, the prob
of one person waiting another for less than
15
min? (14, 18, 116, ...绿皮书)
bution of sample
volatility divided by sample mean?(chi-square,
gamma, F, t)
of (11,11,29,41,41,41)
rd diviation of (11,11,29,41,41,41)
20.25
people are assigned seats but they sitted
randomly, what is the
expected number of
people having original assigned seats: 1, 5, 25?
Stochastic Process & Math Finance
1.
Expected time for Wt to hit boundary +-1 (1)
2. Given zero bond price P(0,T)=1(1+T^2),
forward rate between (T1,T2)?
3. An asset,
(following GBM?) has $$0 dollar value now, $$1 in a
year, what
is the price at t=0.5: 0.5^(0.5),
0.5^(0.75), 0.5, 0.5^(1.25)?
4. Radon-Nikodym
derivative from real prob measure to forward
measure,
with respective of bond price P(0,t)
5. Two independent Brownian motion (Bt, Wt),
starting at point (1,1), what
is the
Probability of this curve hitting positive X-axis
before hitting
negative X-axis? (34)
6.
(Can't remember clearly) Given the process
GBM(r,sigma?) of USDGBP
price in USD risk
neutral measure, what is the GBPUSD in GBP? Drift
term
in choices are (-r, -r-sigma^2,
-r+sigma^2)
7. dudt-5u=0, backward Euler-
method, what choices of dt can make u
unstable: 3,5,8,11,(Can't remember clearly) or
all above?
8. X=exp(Wt), E[X] at t=2? (e)
9. Stock price follows GBM, r = 0.05, sigma =
0.3, spot = 100, prob of
price<50 in one year
from now?
call option, European price = 0.1,
American price: 0.1, 0.2,
0.3, 0.4
3
equivalent measure, P and P',
P(A)=0.5, P(A')=? ( (0,1) )
spot is 10, if
you think one-month later, the price will be 8 and
10 with equal probability, risk-free interest
rate is 5%, what is the price
of call option
strike at 10? (between 51.05 and 101.05 because of
risk-free probability.)
an copula: hazard
rate of A and B are 1% and 2%. A contract pay
you $$1 if A defaults earlier than B. The price
of the contract has lowest
price when the
correlation is (0, 75%, 100%, ...)?
Carlo: to
find out the mean of A, find a variable B,
corr(A,B)=c,
and simulate A + B(E(B)-B)
instead of A. What is B? ( cov(a,b)var(a),
cov(a,b)var(b), 1, -1 )
Carlo: need to
simulate some rare event, so u need to simulate
in a different measure. What is the name of
this technique? (sequential
resampling?)
ce of int(t1,t2) of Wt^2dWt, and some other
ito’s integral
problems
nd-paying stock
(discrete dividend), the price difference of
modeling in GBM and jump-diffusion
Finance (FI and options)
1. Bond: 5%
coupon, (10year?) 1000 face, 6% yield, price?
2. Bond: 3% coupon 10 year bond traded at
par(100), what is the price if
rate goes up
1bp: (99.91, 99.99, 100.01, ...)
3. Which is
higher? FRA vs. Eurodollar futures
4. At 2009,
a trader believes that dividend in 2011 is lower
than
expectation, strategy? longshort 2010
forward and longshort 2011
forward?
5.
(Can't remember clearly) A trader observed that
implied vol of OTM calls
and puts are higher
than that of ATM option, strategy: calendar
spread,
bull spread, bear spread, butterfly?
(I guessed butterfly..)
6. If asset price
positive correlated with interest rate, future
price
is higherlower than forward price?
(higher)
4
7. If interest rate
is deterministic, future price is higherlower than
forward price? (equal)
8. Long long-term
ATM call and short short-term ATM call, adjust the
ratio
to make total vega zero. If before
expiry of the short-term option, spot
= strike
again, vega: positive, negative, zero? (positive?)
trader wants to do a delta-hedge strategy,
but he plugs wrong
sigma1>implied vol, assume
the portfolio is -C+delta*S, what will the
portfolio value change? when the stock
increasedecrease, the value
increasedecrease..
option, increase of delta: (positive,
negative, it
depends, ...)
is the partial
derivative of (time)
of the following is not
Black Scholes assumption: (free borrow
and
lending at risk-free rate, no transaction cost,
same tax rate?...)
lity surface: on the strike
dimension is flat, on the other
dimension, the
vol shape is: 1) increasing function of strike 2)
decreasing with strike 3)frown 4)smile
14.(Can't remember clearly) Condition of
American call being exercised
(I forgot
whether dividend=0 or not)
15.A default
protection seller is longshort credit risk
hedge interest rate risk of 7 year bond of 100MM,
you need to short
2 year bond of? 350MM?
Programming
1. The format of
like
2. static member initialization: simple case
(choose the one initialized
out of the class)
3. static member initialization: In template
class, how many instances?
1) Cannot have
static member in template class 2) only one
instance 3)
as many as instances of classes 4)
as many as instantiations of classes
5
4. static member initialization:
multi-thread case
5. 32-bit computer, non-
optimized code: uint-32 a =16, c = 32, Q:
prinft(
6. space needed to store the number
1,000,000? 17,18,19,20? (20?)
7. Time
complexity of merge sort? ( O(nlogn) )
8.
(Can't remember clearly) Binary tree searching
time with respect of
n?
9. How many
comparisons are needed to sort 5 elements? (4)
ing in 10,000 data costs 1ns, 100,000 data?
(10,35,100,350)
use [ ] in: string, vector,
list, ...(list)
of the following does not
store multiple elements contiguously?
List,
deque, vector, string(list)
* in C is? (null
pointerpointer to nothing?)
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