urgent help needed please

[bcheema]

Hi All,

I have been asked to give my feedback on the questions below as part of internal assessment and this is by someone whom i have been speaking to for a move. I am kind of not sure about the responses below and will be very very thankful if you could help me on your feedback below. if there is some online document which explain some particular response, please post the link. i need to get back in a day and urgently need your help.

1. Consider a simple portfolio with 3 stocks S1, S2 and S3, which follow
lognormal processes with volatility
1,
2 and
3 . Assume S1 and S2 are
correlated with  but that S3 is not correlated with either. Can you compute
the value of a European call which has terminal payoff :
MaxT(S1, S2, S3)

2. Consider a portfolio of 5 risky assets B1, B2, B3, B4
and B5 with annual default probability 0.5% , 1%, 1.5%, 0.5 %, 0.8%
respectively and correlation 25% between any two. Consider a derivative
product which offers a fixed return if all of the assets default in 5 years.
Compute the value of this derivate.

3. Consider a random walker on a cube that blindly chooses one edge at a
time. What is the expected time to the opposite corner?

4. Consider a Weiner process {Wt}. What is the expected time T to reach a
certain value WT=a for the first time? What is the expected time T to reach
either a or ?a?

5. You have a jar containing 999 fair coins and one two-headed coin. You
pick one coin out of the jar and flip is 10 times and get all heads. What is
the probability that the coin you chose is the two-headed one?

6. There are three processes that follow the same SDE:
dSi/Si = μi dt + Voli dW , i = 1,2,3

if S3= S1S2, what is the correlation C12 in terms of Vol1,Vol2,Vol3

7. If S1 and S2 follow the process in question 2, what is the expectation of their
product:
E[S1 S2 ]

8. If the correlation matrix is defined as:


1 p
p 1

What is the Cholesky decomposition of this matrix?

9. The table below shows the call prices determined from an implied vol
surface. Is there arbitrage on the underlying vol surface?

Tenor \ Strike 80% 90% 100% 110% 120%
1M 105.00 88.00 79.00 75.00 77.00
3M 109.04 97.10 85.22 75.76 84.67
6M 109.80 99.84 87.36 76.36 92.14
1Y 116.39 102.15 96.97 78.39 93.11
2Y 121.66 101.91 97.04 92.21 97.08

Thanks Again!!!!!

 

[iHateVariance]

my 2c. i think all of ans u can find on web.
2. need to clarify what u mean by corr 25% (event correlation or factor loading in GC)
4. first hitting time of BM tons of ref on web.
5. standard app of Bayes
6/7 straight forward just do the calcs.
8. 1 0 p sqrt(1-p^2)
9. plug in bs check for monotonicity in maturity and convexity in strike

 

[bcheema]

thanks a lot iHateVariance. i know this might be time consuimg but this will really help me get to the correct solution. will be vert\\y thankful!!

Please please can you give a little more detailed response on a few. It will really help me get started in the correct direction.

1. read garbare and others docs but i am not sure how detailed the workling should be and what kind of repsonse are they expecting

2. I am not sure about what the correlation is. that is how the question is phrased. can you please give me some guidance on this.

6,7- pleaaaase can you add in just a few steps of the initial working. thanks!

9. same here please. juts a few steps of initial working

 

[iHateVariance]

1. http://www.finmod.co.za/3assetrainbow.pdf u can always do MC(with control variate) if they want just number. since they made 3rd stock independent i think they want u to use it as numeraire and to work out formula. then u need to do few dble integrals and ur answer will look similar to Graeme's with bivariate normal instead dnt have details though.
2. google one factor Gaussian copula. easiest is to do is MC(again u can do clever MC with importance sampling Glasserman has a few chapters on that). but usually ppl condition and then integrate out common factor numerically.
7. if s1 and s2 independent then E(s1s2)=E(s1)*E(s2)
9. i see arb in 6m, 1y and 2y. http://www.ederman.com/new/docs/laughter.html

 

[joel_b]

Isn't the point of the assignment to prove you can do the work if you were to make the move?

 

[bcheema]

Isn't the point of the assignment to prove you can do the work if you were to make the move?

no its given just for me to research and demonstrate my learning and understanding.

Anyways

all, please kindly keep your inputs coming . that will be really appreciated. thanks!

 

[alain]

no its given just for me to research and demonstrate my learning and understanding.

exactly, to demonstrate that you can do the job. Now it's clear why you haven't been able to go forward.

 

[bcheema]

exactly, to demonstrate that you can do the job. Now it's clear why you haven't been able to go forward.

Thanks for the helpful comments.