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Topic Title: Interview Questions
Created On Wed Aug 27, 03 05:30 PM
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GM
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Wed Aug 27, 03 05:30 PM
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Here are some of the technical questions I was asked at a recent quant interview:

1. What is the limit of (x^2 + x)^0.5 - x as x tends to infinity?
2. Current stock price is 100. In the next period, it can go up to 150 with probability 0.9, or down to 90 with probability 0.1. How much is a one period call with strike 130 worth if the risk free rate is zero?
3. y'' + y' + y = 0
i) what is the general solution? [Answer: Ae^(alpha*t)]
ii) solve for alpha
iii) factorise out the real component of the solution
iv) do you recognise the resulting function?

Please show working so that I can check my logic!
 
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phirangm
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Wed Aug 27, 03 08:03 PM
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why do they demand ph. d's and then ask q's that would barely strain an undergrad?

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robertral
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Wed Aug 27, 03 08:05 PM
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Quote

Originally posted by: GM


2. Current stock price is 100. In the next period, it can go up to 150 with probability 0.9, or down to 90 with probability 0.1. How much is a one period call with strike 130 worth if the risk free rate is zero?
q]

Answer to 2, i think, is C = exp(0)*[0.9*20 + 0.1*0] = 18

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Alainniala
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Wed Aug 27, 03 08:19 PM
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Why are you using the probabilities given as being the risk neutral ones?
 
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robertral
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Originally posted by: Alainniala
Why are you using the probabilities given as being the risk neutral ones?


How else would you do it from the info given?

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Alainniala
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Wed Aug 27, 03 09:16 PM
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up move: 1.5
down move: 0.9

--> Risk neutral probability = (1-0.9)/(1.5-0.9) = 0.17 = risk neutral prob of going up

and then use 0.17 and (1-0.17) as your probabilities...
 
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robertral
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Wed Aug 27, 03 09:23 PM
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Cool, thanx, yeah just had a look at the Hull book on it.
I always forget the easier stuff when I'm looking at the harder stuff :S -> that's my excuse lol


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leibniz99
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if you find these difficult you are wasting your time applying for quant jobs.
 
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SauceDrinker
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Thu Aug 28, 03 11:01 AM
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1. +0.5 multiply by conjugates.
2. 20/6.
3. See undergrad DE book.

 
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silverside
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Thu Aug 28, 03 11:38 AM
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For 1) I would have done it by simplifying and getting the Taylor expansion of root(1+1/x) around 1; The constant term then falls out at 1/2.
 
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robertral
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Originally posted by: leibniz99
if you find these difficult you are wasting your time applying for quant jobs.


Who said I was applying for quant jobs? ;-)

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leibniz99
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Thu Aug 28, 03 01:28 PM
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Quote

Originally posted by: GM
Here are some of the technical questions I was asked at a recent quant interview:





 
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robertral
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Thu Aug 28, 03 01:44 PM
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I thought I'd have a go at answering them. It doesn't mean that I'm applying for quant jobs

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Edited: Thu Aug 28, 03 at 01:45 PM by robertral
 
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kr
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Thu Aug 28, 03 02:38 PM
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on the ode problem, recall that the 'rates' in the exponential terms coincide with the roots of the polynomial over C... that's because if you put
f(t;r) = e^rt as your generic solution and then think of it as a function of r rather than t, this transformation turns differentiations into powers of r. So then you need the roots of

r^2 + r + 1

i.e. r = (-1 +/- i.sqrt(3)) / 2 and the solution has sine and cosine terms attached to an exponential decay etc.

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MinusTheBaboon
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Thu Aug 28, 03 03:25 PM
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1/
1/2 - multiply top and bottom (x^2 + x)^0.5 + x

So
((x^2 + x)^0.5 - x) ((x^2 + x)^0.5 + x)
--------------------------------------------------
((x^2 + x)^0.5 + x)

=

x^2 + x - x^2
------------------------
((x^2 + x)^0.5 + x)

=

x
-----------------------
((x^2 + x)^0.5 + x)

The denominator goes to 2x. x/2x->1/2
 
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kr
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Thu Aug 28, 03 03:40 PM
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why work so hard when (1+x)^0.5 = 1 + x/2 + O(x^2) as x->0? (i.e. Taylor)

We have (x^2 + x)^0.5 = x . (1 + 1/x)^0.5 = x(1 + 1/2x + O(x^-2)) = x + 1/2 + O(1/x).



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Gerasimos
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Thu Aug 28, 03 03:54 PM
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Quote

Originally posted by: robertral
Quote

Originally posted by: Alainniala
Why are you using the probabilities given as being the risk neutral ones?


How else would you do it from the info given?


Why wouldn't you? Risk neutral world valuation gives the same results as real world since the risk preference
is not involve. That is the method used for pricing derivatives using binomial trees anyway even for complex problems,
not for this straightforward one.

Also in q3 the CP has 2 complex roots so y=Aexp(k1*x) + Bexp(k2*x)

 
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GM
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Fri Aug 29, 03 09:47 AM
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1. The limit is 1/2, either Taylor series expansion or multiplying top and bottom by (x^2 + x)^0.5 + x would be fine I'm sure.
2. 10/3 is correct, you have to use risk neutral probabilities.
3. alpha = (-1 +/- sqrt(3).i)/2, so two conjugate complex roots, then factoring out exp(-t/2) from the general solution you are left with a cosine function. Afraid to say my answer wasn't quite as elegant as kr's!
 
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Graeme
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Don't give this guy the answers!!!! It is him they are asking the questions, and it is him applying for the job, not the Wilmott community!

On a similar issue, one sees in the student forums numerous waves of questions, posted by the same person, which, when put together, look suspiciously like (the non-trivial part of) a tutorial for a maths of finance degree course from somewhere. The same sentiment applies, the tut is for the student, not for the world at large. Let the student find the answers in books, the internet, plain hard work .. but not by saying 'help please' at Wilmott and then people showing how smart they are during their lunchbreak!



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Alainniala
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Sun Aug 31, 03 01:28 PM
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I think that's a very selfish and nerd-like attitude...
 
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