Financial contract

JohanL

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.

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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.

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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)

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Investment =

951000


Value12Quarters =

1.1660e+06


Value20Quarters =

1.3947e+06


AnnualReturnPercentAfter12Q =

7.0302


AnnualReturnPercentAfter20QExpiration =

7.9592