Index Arbitrage

Discussion in 'Options' started by Durian, Dec 19, 2007.

  1. Durian

    Durian

    Yes, I realize that, thanks for the tip
     
    #11     Dec 20, 2007
  2. Durian

    Durian

    Oh and I am a little baffled on the Greeks too, since the stocks selected for the replication accounts for about 50% of the index, not sure what should be done to adjust this or will it just be a matter of trading double to make the replicated basket equating to 100% of the index.
     
    #12     Dec 20, 2007
  3. segv

    segv

    #13     Dec 20, 2007
  4. You can build a big similarity matrix that has the correlation between each of n stocks in the index with every other. Then, it's a matter of solving the following problem:

    - where ρ(i, j) is the correlation (similarity) between two stocks
    - where x(i, j) is binary: 1 if stock i is 'represented' by stock j

          n    n
    max Σ   Σ ρ(i,j) * x(i,j)
          i=1 j=1

    subject to the following constraints:

    n
    &Sigma; x(i, j) = 1 for i = 1, ...n <-- every stock i is represented by some stock j
    j=1

    n
    &Sigma; y(j) = K <-- y is binary, choose only K stocks
    j=1

    x(i, j) <= y(j) for i,j = 1,...,n <-- stock i is represented by at most one stock j

    So - I think that's basically how you choose the best stocks to represent the whole group, theoretically. Transaction costs, how frequently you'll be rebalancing, and how closely you need to match the index will be factors to consider when you decide how many stocks you'll use in order to replicate the index.

    You can do small indices this way in Excel using Solver. Bigger ones you can probably use some of the free solvers and modeling languages from coin-or.org (I'm going to try some stuff with FlopC++ and CLP).

    I'd like to do some more in-depth stuff along these lines for an internship this summer (I'm finishing an MBA program) and I have a few ideas I'd like to execute at a prop options firm. If anyone has any leads, please give me a PM.
     
    #14     Dec 20, 2007
  5. rosy2

    rosy2

    google for principal component analysis
    or factor analysis
     
    #15     Dec 22, 2007