MATLAB: Do “bndyield” and “cfyield” give different results

Financial Toolbox

I have some code to calculate bond yield ("bndyield"), and I set up very similar code to calculate the same yield using the cash flow yield, "cfyield" function. For some reason, I am getting different results. What might be causing this?

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The primary issue here is the treatment of accrued interest. Specifically, "bndyield" accepts a clean price as an input, internally computes the accrued interest and adds that to the clean price to compute a full price before computing the yield to maturity. Therefore, to compare the outputs from the two approaches, the input cash flows to "cfyield" should include the accrued interest as well.

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MATLAB: What is the difference between IMPVBYBLS and BLSIMPV, and how to I determine the Black-Scholes implied volatility using these functions

Both IMPVBYBLS and BLSIMPV use the Black-Scholes model to compute the implied volatility for a given option price. However, one of the main differences between the two functions is that IMPVBYBLS allows specifying cash dividends as well as continuous dividend yields, while BLSIMPV only allows continuous dividend yields.

If you specify continuous dividend yields for both IMPVBYBLS and BLSIMPV, they produce the same results:

Strike = 29;
AssetPrice = 30;
Sigma = .25;
Rates = 0.05;
Settle = datenum('01-Jan-2008');
Maturity = datenum('01-May-2008');
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, ...
'EndDates',Maturity, 'Rates', Rates, 'Compounding', -1,'Basis',1);
DividendType = {'continuous';'continuous'};
DividendAmounts = [0.05; 0.045];
ExDividendDates = {NaN;NaN};
StockSpec = stockspec(Sigma, AssetPrice, DividendType, DividendAmounts);
OptSpec = {'call'; 'put'};
OptionPrice = optstockbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike);
ImpvVol1 = impvbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, ...
Strike, OptionPrice)
ImpvVol2 = blsimpv(AssetPrice, Strike, Rates, ...
yearfrac(Settle,Maturity,1), OptionPrice, 'Class', OptSpec,'Yield',DividendAmounts)
ImpvVol1 =
0.250000000000000
0.250000000000000
ImpvVol2 =
0.250000000000000
0.250000000000000

MATLAB: Does SWAPBYZERO include the principal in its computation of the Interest Rate Swaps in MATLAB (R2013b)

As mentioned in the documentation (R2013b), the "Principal" parameter is a "notional" amount used to determine the cash flows, although there is no actual exchange of principal. So you should not set this parameter to zero. Although the cash flow outputs "RecCF" and "PayCF" do include principal amounts, this should not affect the computation of the swap price since the principal amounts in the two legs cancel each other out.

If you have access to John Hull textbook "Options, futures, and other derivatives", it is mentioned that:

"If the principal were exchanged at the end of the life of the swap, the nature of the deal would not be changed in anyway. The principal is the same for both the fixed and the floating payments. Exchanging $100 million for $100 million at the end of the life of the swap is a transaction that would have no financial value...."

An enhancement request has been submitted so that the cash flow outputs, "RecCF" and "PayCF", not include the notional principal at the end of the swap to reflect the actual mechanics of the swap.

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Related Solutions

MATLAB: What is the difference between IMPVBYBLS and BLSIMPV, and how to I determine the Black-Scholes implied volatility using these functions

MATLAB: Does SWAPBYZERO include the principal in its computation of the Interest Rate Swaps in MATLAB (R2013b)

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