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  1. Brad Warren

    Best Strategy

    You can't do better than zero in expectation. You're playing a game at even odds with a fair coin. You have no advantage.
  2. Brad Warren

    Baruch MFE Spring 2012 Baruch MFE Facebook Contest

    Congratulations to the winners!
  3. Brad Warren

    Phone Interview for Quant Summer Internship

    Well if it's for a quant job, I would be surprised if they didn't ask any technical questions at some point. But it sounds like this call is just a brief interview for you to talk about your background. And think of some questions to ask too.
  4. Brad Warren

    two interview questions

    Another way from 2 to 3: x^-1, cos^-1, tan, x^2
  5. Brad Warren

    improving rolls of a die

    I like your solution. But to get the odd k terms (for Player 1 winning), you should actually add the binomial powers, and then we need to divide by a factor of 2. The probability should be...
  6. Brad Warren

    improving rolls of a die

    That formula works for n=2. But the game can go on more than 2 rolls. This one works for n <= 6: (\frac{79n^4+10n^3+5n^2+50n-24}{120n^4}) but I don't see a pattern for the general solution.
  7. Brad Warren

    Competing with MFE grads?

    I interned in Technology at an investment bank last summer. I'm a junior too, so I'm trying to get a quant internship this summer. I'm not sure exactly what I want to do yet, which is another reason to get experience in a quant internship. This firms list is a good starting point. I've found a...
  8. Brad Warren

    Competing with MFE grads?

    I'm in a similar situation as you. I would recommend self-study to try and improve on the areas you feel are lacking. I'm planning on applying for jobs as well as MFE, and then the decision depends on what job I can get.
  9. Brad Warren

    Competing with MFE grads?

    I don't see anything negative about athletics. Especially at the collegiate level, it requires a significant amout of discipline and time. If someone has the same academic record and technical skills as other candidates, and they were able to do that while spending hours every day at practice...
  10. Brad Warren

    Sampling Correlated Asset Paths

    You could do it either way. Starting with a vector of uncorrelated standard normals, using the covariance matrix is more direct since you have to factor in the individual volatilities anyway.
  11. Brad Warren

    Quantitative Interview questions and answers

    An alternative solution: For a Brownian motion, there is equal probability that Wt = a or Wt = -a. Taking the average, (1/2(N(a)+N(-a))=1/2)
  12. Brad Warren

    Santas at Christmas party

    For G(4,4), there are 2 groups of 4 such that all santas are friends with everyone in the other group. For G(4,3), there are 4 santas in GROUP 2 that each need to have 3 friends in GROUP 3, but they must also have only 2 mutual friends in GROUP 3 (the third mutual friend is the first santa)...
  13. Brad Warren

    Santas at Christmas party

    There are \(\frac{nk}{2}=\frac{k}{2}(1+k+\frac{k(k-1)}{l})\) edges. Either k or \(\frac{k(k-1)}{l}\) has to be even. I think those conditions are sufficient. Never mind, that doesn't explain why G(4, 3) doesn't exist. But k does not have to be even.
  14. Brad Warren

    Double barrier, ctd...

    It hits both barries before reaching time T, not at the same time.
  15. Brad Warren

    poisson cars

    The process is Markov, so we can condition on the next car passing. The time to cross the road is 20 seconds if no cars pass for 20 seconds. Otherwise, the expected time to cross is the time the car passes plus the original expectation. The time a car passes is distributed as Exp(lambda = 1/10)...
  16. Brad Warren

    NYC Drinks - QuantNet meet up?

    Did we decide on a place?
  17. Brad Warren

    List of sample questions for Quant Interviews

    Since the barriers are not symmetric about zero, the distribution for the random walk won't be either, so the probability of being > 0 is not 1/2. The probability is dependent on time. Immediately after time 0, the probability will be 0.5 because there is no chance of hitting the barrier. As...
  18. Brad Warren

    Proper Procedure for Calculating Sortino Ratio

    You should use the total number of observations. The downside risk should be less if there is a smaller number of observations below the target return.
  19. Brad Warren

    New Courses being offered by Stanford in Jan,2012

    They added a few more courses. I didn't see Cryptography or Design and Analysis of Algorithms last time I checked.
  20. Brad Warren

    The Official Undergraduate Discussion Thread

    Also, I think work experience can be very beneficial. Both for your resume and for trying to figure out what you really want to do. I'm looking for an internship to get some quant experience.
  21. Brad Warren

    The Official Undergraduate Discussion Thread

    Next year will be my final year of undergrad. I'm a CS major, but I've tried to add as much math and finance as I can since I learned about quantitative finance last year. This semester, I'm taking: Concurrent Programming Artificial Intelligence Object-Oriented Analysis & Design Probability...
  22. Brad Warren

    An Interview Question

    \(\beta=\frac{Cov(r, r_m)}{Var(r_m)}=\rho\frac{\sigma}{\sigma_m}\) Therefore, \(\sigma=\frac{\sigma_m}{\rho}\) And the median stock price is above 20 iff \(\mu-\frac{1}{2}\frac{\sigma_m^2}{\rho^2}>0\) So the stock price is more likely to go up for a higher correlation and less likely for...
  23. Brad Warren

    What is this option ???

    It shouldn't be difficult to price with MC or finite differences. I think you could get an analytical formula using the bivariate Normal distribution.
  24. Brad Warren

    List of sample questions for Quant Interviews

    Having at least 2 birthdays the same is the complement of no one sharing a birthday: \(P=1-\frac{365}{365}\frac{364}{365}...\frac{365-n+1}{365}=1-\frac{365!}{(365-n)!365^n}\) The probability exactly two people share the same birthday is the probability only the first 2 people do multiplied by...
  25. Brad Warren

    List of sample questions for Quant Interviews

    The probability should be greater than 0.5 because -2 is closer to 0 than 3. The process is a martingale. Its expectation at any future time is 0. Let us use the expectation in terms of the probability of hitting -2 first, at the time it hits either -2 or 3. 0 = -2p + 3(1 - p) p = 3/5 I...
  26. Brad Warren

    Programming || Math

    I would say go with Financial Math and minor in CS. Although you may be able to meet the minimum requirements and get by with one programming class, it will certainly make your life easier if you have more programming experience. If you complete the minor and find yourself wanting more, you...
  27. Brad Warren

    List of sample questions for Quant Interviews

    Well in that case then I would probably look at the downside risk and use some risk-adjusted measure to evaluate the trade.
  28. Brad Warren

    List of sample questions for Quant Interviews

    If I know the host always opens another door, then I would switch. But maybe he does it only because I picked the right door.
  29. Brad Warren

    List of sample questions for Quant Interviews

    I think if I work on an arbitrage desk, I'm not making a trade with a 49% chance of a loss.
  30. Brad Warren

    Probability of Discovering (N-1)st Point on a Circle

    The second set is for r - 1: \(P(r+1)=\frac{r}{(N-2)(N-3)}\) , \(r\leq2\) \(P(r+1)=\frac{N}{(N-2)(N-3)}\) , \(2<r\leq N-3\) \(P(r+1)=\frac{N-r}{(N-2)(N-3)}\) , \(r>N-3\) \(P(r-1)=\frac{r-2}{(N-2)(N-3)}\) , \(r\leq4\) \(P(r-1)=\frac{N}{(N-2)(N-3)}\) , \(4<r\leq N-1\)...
  31. Brad Warren

    Probability of Discovering (N-1)st Point on a Circle

    Huh, I posted it twice, edited one, and now the other is gone. The probabilities of the (N-2)-nd point being r + 1 or r - 1 are: \(P(r+1)=\frac{r}{(N-2)(N-3)}\) , \(r\leq2\) \(P(r+1)=\frac{N}{(N-2)(N-3)}\) , \(2<r\leq N-3\) \(P(r+1)=\frac{N-r}{(N-2)(N-3)}\) , \(r>N-3\)...
  32. Brad Warren

    Probability of Discovering (N-1)st Point on a Circle

    I assume the points are ordered 1 to N, we start at point 1, the (N – 2)-nd distinct point is the point we reach such that there are 2 points we have not visited, and the starting point counts as visited. Let X(t) be a stochastic process such that X(0) = 0 and it either increments or decrements...
  33. Brad Warren

    dice game

    They are not the same
  34. Brad Warren

    Second BS or MS Please Help!

    If you're planning on doing an MFE, do you really need another degree? You can self-study and take a few extra courses to build your profile.
  35. Brad Warren

    strengthening my background and other questions...?

    More programming experience would be helpful too. Maybe take a look at http://www.quantnet.com/forum/threads/c-online-certificate-for-mfe-applicants.6297/
  36. Brad Warren

    Yield curve non parallel shifts - spline

    So the error minimization essentially aggregates the market data into a base term structure defined by one rate at each knot. Then this curve is used for normal spline interpolation. Thanks for clearing that up.
  37. Brad Warren

    Yield curve non parallel shifts - spline

    Hey Bob, You said in class that you might fit a spline without constraining it to perfectly match market prices, e.g. using least-squares. Does that make any difference? How would you go about shocking this curve? Do you just move the knots and fit a spline to intersect them all, or would...
  38. Brad Warren

    Yield curve non parallel shifts - spline

    I suppose even if the shift is non-polynomial, you could still add it to the segments if it has a continuous second derivative. You would still have a smooth, though not polynomial, spline.
  39. Brad Warren

    Yield curve non parallel shifts - spline

    If you could express the shift as a polynomial of the same degree as the spline, then just add the shift to each segment and there are no issues.
  40. Brad Warren

    Yield curve non parallel shifts - spline

    A shift at a single point will affect the entire curve because of the constraint of continuous derivatives. So you can't really have an isolated shock of one part of the curve.
  41. Brad Warren

    Program Chances

    Brand name is not a requirement to get into a top program. Quit thinking with the mindset that you are at a disadvantage! Continue to excel at your school, and learn as much as you can about the field. Try to figure out what it is you want to do, what are your strengths, and what are your...
  42. Brad Warren

    Hull White - Interest rate tree model

    You want calibrate the model to market bond prices, e.g. fitting the parameters to minimize the squared errors between the model output and the market yield curve.
  43. Brad Warren

    Question about pursuing MFE.

    I'm not an expert, but here's my 2 cents. You certainly do not need an MBA for quantitative finance. Technical math and programming skills are more important than finance knowledge. Not saying you should neglect finance, but it is easier to pick up than the other skills. That said...
  44. Brad Warren

    Why did you choose Quantitative Finance?

    In addition to an interest in the markets, I enjoy math, and want to be able use it for practical applications.
  45. Brad Warren

    What apps you have on your Android/iPhone?

    WSJ EasyTether - great for traveling or when I don't have WiFi access
  46. Brad Warren

    Implied Volatility Bias

    The volatility skew is a well-known phenomon indicating the market does not believe that returns are lognormal. The BS implied vol is just the wrong number you put in the wrong formula to give you the "right" (market) price. Attempts to address the limitations of Black-Scholes include...
  47. Brad Warren

    What Sorts of Jobs Will a Math/ Stat Masters From a State School Get You?

    I think the ability to convey your knowledge and qualifications (given you have them, of course) would be the most important thing when being considered for a job...or when applying to top-tier grad programs.
  48. Brad Warren

    Best instrument/method for speculation?

    OTM calls will give you more leverage, e.g. more delta for each dollar invested. Though it will cost you more in theta decay, as iHateVariance said.
  49. Brad Warren

    NYC Drinks - QuantNet meet up?

    31st works for me
  50. Brad Warren

    NYC Drinks - QuantNet meet up?

    Looking forward to it! I turned 21 since the last one.
  51. Brad Warren

    Euler discretization for Monte Carlo Simulation

    No, the standard deviation is proportional to the sqrt of the timestep. The problem is you only have one variable X and you sum all the runs. You need to record the result after each run and start with X at zero again.
  52. Brad Warren

    Brokers

    I haven't seen anything on the site about foreign markets, but I've never tried to trade anything outside the US.
  53. Brad Warren

    Brokers

    I use OptionsHouse. They have a flat rate for stocks of 3.95 (I was grandfathered in at the old rate of 2.95). For options, it's $1 a contract for the first 10 (15 for spreads) and then it's only 0.15 per contract after that.
  54. Brad Warren

    What books are you currently reading?

    A Primer for the Mathematics of Financial Engineering My Life as a Quant
  55. Brad Warren

    MFE vs. MS Computer Science?

    Is a PhD really a requirement to do strats/modeling? I've heard people say you shouldn't do a PhD for career goals, only if you're interested in academia.
  56. Brad Warren

    How did you know about Quantnet

    I just stumbled on it using Google. I think I was searching "quantitative finance" or "quant masters programs."
  57. Brad Warren

    Drug addict

    Let E(n, m) be the expected maximum number of half pills after starting with n whole pills and m half pills. The answer we're looking for is E(n, 0). I tried to solve for it in terms of E(n-1, 0). This is as far as I got: E(n, 0) = 2/(n^2 (n-2)!) + (1 - (n-1)(n-2)/n^2)E(n-1, 0) + (n-1)(n-2)/n^2...
  58. Brad Warren

    Baruch MFE Baruch MFE Facebook Contest

    Thanks for holding the contest. I had fun.
  59. Brad Warren

    New Quantnet members say hi

    Hi, My name is Brad Warren. I'm a computer science major at Stevens Institute of Technology graduating in 2013. Last year, I was introduced to quantitative finance and I really enjoy it. I think it is a great way to combine my skills in math and programming, and now I aspire to be a quant...
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