MATLAB: What function do I use to price a Callable Zero Coupon Bond in the Financial Derivatives Toolbox 5.4 (R2009a)

MATLAB

I want to find the price of a Callable Zero coupon bond. I know that there are functions for pricing Callable Bonds in general but I couldn't find one for Zero Coupon Callable Bond.

Best Answer

Zero Coupon Callable Bonds are the same as Callable Bonds, with Coupons set zero. Hence, we can use the functions for pricing Callable Bonds (such as OPTEMBNDBYBDT), set the 'Coupons' and 'Periods' parameters to zero, specify Excercise dates and get the price of a Zero Coupon Callable Bond. An example code is attached.

Related Solutions

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: Is there any additional information available about the derivative price inputs to the Black-Scholes functions in the Financial Toolbox

The "Q" parameter for the Black-Scholes functions in the Financial Toolbox is the annual dividend rate expressed as a percentage of the price of the security. The equations we use are the Black-Scholes equations from "Options, Futures, & Other Derivatives" by Hull -- you can verify this by opening and viewing the function by entering the command:

edit blsprice

Consider the following example that explains the dividend parameter:

The S&P 100 index currently stands at 696 and has a volatility of 30% per annum. The risk-free rate of interest is 7% per annum and the index provides a dividend yield of 4% per annum. Calculate the value of a three-month European put with strike price 700.

This problem can be solved using the following call to the BLSPRICE function:

[Call, Put] = blsprice(696, 700, .07, .25, .3, .04)

which produces the result:

 Call =
    41.7720
 Put =
    40.5539

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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: Is there any additional information available about the derivative price inputs to the Black-Scholes functions in the Financial Toolbox

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