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Financial contract

  1. Jun 14, 2012 #1
    I havent used matlab in many years.

    I have been trying to estimate the value
    of a financial contract my bank is selling.

    It would be great if someone has the time to read it through and check
    if i have made any mistakes.

    ***********************************


    Its price today is 95.1 and it expires in 5 years and you can
    sell it back to the bank at at least a 100 at expiration.
    100 was the starting price for the contract.
    You can also buy and sell the contract on the market at any time.

    You get a rate of return of 1.953% on your investment each quarter.

    The contract is for a specific company and if this company has
    a credit event you get back between 0 and 40% of your investment.
    I assumed a uniform distribution between 0 and 40%.

    From my data i have estimated the probability of a credit event
    in any quarter to be 0.0031578.

    I also assumed the credit events happen at end of a quarter.

    Today you buy the contract at a 4.9% discount which you get back at
    the expiration date.

    ******************************************


    clear

    format long


    PCEQ = 0.0031578; % Probability of a Credit Event for a given Quarter

    PNoCEQ = 1-PCEQ;

    NOC = 10000; % Minimum Number Of Contracts

    Price = 95.1; % Price per contract

    Inv = Price*NOC; % Total investment

    RoRQ = 1.019351; % Rate of Return for each Quarter

    Q = 5*4; % Number of Quarters to expiration

    spread = 0.2*NOC;

    value(1)=Inv-spread;



    for j=1:10000

    for i=1:Q

    r = 0 + (0.4-0).*rand(1,1);
    ReturnAtCE = value(1)*r;
    % Return At Credit Event is value(1) times
    % a random number between 0 and 0.4 from a uniform PD.


    value(i+1) = value(1)*RoRQ^(i)*PNoCEQ^(i)+(ReturnAtCE+value(1)*RoRQ^(i)-value(1))*(1-PNoCEQ^(i));
    % Value of investment after each quarter
    % I assume the credit events happens at the end of each quarter so you get
    % a return of ReturnAtCE + the rate of return for the number of
    % quarters since the start

    end


    value(Q+1)=value(Q+1)+4.9*NOC;
    % Today you buy the contract at a 4.9% discount which you get back at
    % expiration


    value1(j,1:(Q+1)) = value;
    % Because i picked random numbers from a uniform PD i calculate
    % the values 10000 times and then on line 56-60 i take the average.

    end


    for m=1:(Q+1)
    value2(m) = sum(value1(:,m));
    end


    value2 = value2/10000

    commision = 59*2;

    value2 = value2 - commision;



    format short

    Investment=Inv

    Value12Quarters = value2(13)

    Value20Quarters = value2(Q+1)

    PercentChange12Q=1+(Value12Quarters-Inv)/Inv;

    PercentChange20Q=1+(Value20Quarters-Inv)/Inv;

    AnnualReturnPercentAfter12Q = 100*(nthroot(PercentChange12Q, 3)-1)

    AnnualReturnPercentAfter20QExpiration = 100*(nthroot(PercentChange20Q, 5)-1)

    *****************************

    Investment =

    951000


    Value12Quarters =

    1.1660e+06


    Value20Quarters =

    1.3947e+06


    AnnualReturnPercentAfter12Q =

    7.0302


    AnnualReturnPercentAfter20QExpiration =

    7.9592
     
    Last edited: Jun 14, 2012
  2. jcsd
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