MATLAB: How to get more information on method used for the calculation of discount factors for FIXEDBYZERO function in Financial Derivatives Toolbox R2007b (5.1)

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I need information on calculation of discount factors in valuation of fixed income securities with functions like fixedbyzero. Specifically, which method (e.g., linear interpolation, logarithmic inteerpolation, cubical splines, bootstrapping etc.) is used to calculate discount factors.

Best Answer

Interpolation is done only if necessary. If the time periods corresponding to the rates passed into the functions via RateSpec, coincide with those needed to discount the instrument’s cash flows, then interpolation will not be necessary and discount factors can be calculated directly. This is typically done via the function RATE2DISC. For more information about RATE2DISC, type the following command at the MATLAB Command prompt:

doc rate2disc

Now, if the rates are not zero rates, or the zero dates do not correspond to those of the instrument's cash flow dates, then interpolation will be necessary. This interpolation needs to respect the original discount factors implicit in the specified interest rate term structure (RateSpec), so a combination of optimization and linear interpolation is used. All of these calculations are done inside the function RATETIMES. For more information about RATETIMES, type the following command at the MATLAB Command prompt:

doc ratetimes

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It is possible to try to use short interest rate trees to build up pricing functions for more complex interest rate derivatives like swaptions.

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MATLAB: How to convert interest rates from one day count and frequency to another using Financial Derivatives Toolbox 5.2 (R2008a)

You can convert interest rates from one day count to another and from one frequency to another as below. The code first converts the given interest rate to a discount factor, and then uses the discount factor to convert to interest rate. During each conversion we specify different day count and frequency.

% Dummy dates for calculation purpose
StartDates = ['15-Feb-2000'];
EndDates  = ['15-Aug-2000'];
% Specify Frequency and Date Basis for Old Interest Rate
Compounding_old = 2;
ValuationDate = ['15-Feb-2000'];
Rates_old = [0.05];
Basis_old = 1; % 30/360 (SIA)
% Obtain Discount Factor
Disc = rate2disc(Compounding_old, Rates_old, EndDates, StartDates, ValuationDate, Basis_old);
% Specify Frequence and Date Basis for New Interest Rate
Compounding_new = 4;
Basis_new = 2; % For actual/360
% Obtain New Interest Rate
Rates_new = disc2rate(Compounding_new, Disc, EndDates, StartDates, ValuationDate, Basis_new)

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MATLAB: Is there a function or method for interest rate swaption evaluation

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