Fixed-Income Toolbox™

cbprice - Price convertible bond

Syntax

[CBMatrix, UndMatrix, DebtMatrix, EqtyMatrix] = 
cbprice(RiskFreeRate, StaticSpread, Sigma, Price, ConvRatio, 
NumSteps, IssueDate, Settle, Maturity, CouponRate, Period, Basis, 
EndMonthRule, DividendType, DividendInfo, CallType, CallInfo, 
TreeType)

Arguments

`RiskFreeRate`	Annual yield of risk-free bond with the same maturity as the convertible, compounded continuously. (Recommended value is the yield of a risk-free bond with the same maturity as the convertible.)
`StaticSpread`	Value of constant spread to the risk free rate. Adding this to the `RiskFreeRate` produces the issuer's yield, which reflects its credit risk.
`Sigma`	Annual volatility in decimal.
`Price`	Price of asset at settlement or valuation date.
`ConvRatio`	Scalar. Number of assets convertible to a single bond.
`NumSteps`	Number of steps in binomial tree.
`IssueDate`	Issue date of bond.
`Settle`	Settlement date of bond.
`Maturity`	Maturity date of bond.
`CouponRate`	Coupon rate payable per unit of face value.
`Period`	(Optional) Coupons per year of the bond. A vector of integers. Allowed values are 0, 1, 2, 3, 4, 6, and 12. Default = 2.
`Basis`	(Optional) Scalar value for day-count basis of the instrument. 0 = actual/actual (default) 1 = 30/360 (SIA) 2 = actual/360 3 = actual/365 4 = 30/360 (PSA) 5 = 30/360 (ISDA) 6 = 30/360 (European) 7 = actual/365 (Japanese) 8 = actual/actual (ISMA) 9 = actual/360 (ISMA) 10 = actual/365 (ISMA) 11 = 30/360E (ISMA) 12 = actual/365 (ISDA)
`EndMonthRule`	(Optional) End-of-month rule. This rule applies only when `Maturity` is an end-of-month date for a month having 30 or fewer days. 0 = ignore rule, meaning that a bond's coupon payment date is always the same numerical day of the month. 1 = set rule on (default), meaning that a bond's coupon payment date is always the last actual day of the month.
`DividendType`	(Optional) 0 = dollar dividend (default). 1 = dividend yield.
`DividendInfo`	(Optional) Two-column matrix of dividend information. First column contains the ex-dividend date corresponding to the amount in the second column. Default = no dividend.
`CallType`	0 = call on cash price (default). 1 = call on clean price.
`CallInfo`	(Optional) Two-column matrix of call information. First column contains the call dates. Second column contains call prices for every $100 face of bond. A call in the amount of call prices is activated after the corresponding call date. Default = no call feature.
`TreeType`	(Optional) 0 = binomial tree (default). 1 = trinomial tree.

All inputs are scalars except for DividendInfo and CallInfo.

Description

[CBMatrix, UndMatrix, DebtMatrix, EqtyMatrix] = cbprice(RiskFreeRate, StaticSpread, Sigma, Price, ConvRatio, NumSteps, IssueDate, Settle, Maturity, CouponRate, Period, Basis, EndMonthRule, DividendType, DividendInfo, CallType, CallInfo, TreeType) computes the price of a convertible bond using a Cox-Ross-Rubinstein binomial tree or, optionally, a trinomial tree.

CBMatrix is a matrix of convertible bond prices.

UndMatrix is a matrix of stock prices in binomial format.

DebtMatrix is a matrix of the debt portion of the convertible bond.

EqtyMatrix is a matrix of the equity portion of the convertible bond.

Examples

Perform a spread effect analysis of a 4%-coupon convertible bond callable at 110 at the end of the second year, maturing at par in 5 years, with yield to maturity of 5% and spread (of YTM versus 5-year treasury) of 0, 50, 100, and 150 basis points. The underlying stock pays no dividend.

RiskFreeRate = 0.05;
Sigma        = 0.3;
ConvRatio    = 1;
NumSteps     = 200;
IssueDate    = datenum('2-Jan-2002');
Settle       = datenum('2-Jan-2002');
Maturity     = datenum('2-Jan-2007');
CouponRate   = 0.04;
Period       = 2;
Basis        = 1;
EndMonthRule = 1;
DividendType = 0;
DividendInfo = [];
CallInfo     = [datenum('2-Jan-2004'), 110]; 
CallType     = 1;
TreeType     = 1;   
    
% Nested loop accross prices and static spread dimensions
% to compute convertible prices.
 
for j = 0:0.005:0.015;
StaticSpread = j;
      for i = 0:10:100
          Price = 40+i;
          [CbMatrix, UndMatrix, DebtMatrix, EqtyMatrix] = ...
           cbprice(RiskFreeRate, StaticSpread, Sigma, Price, ...
           ConvRatio, NumSteps, IssueDate, Settle, ...
           Maturity, CouponRate, Period, Basis, EndMonthRule, ...
           DividendType, DividendInfo, CallType, CallInfo, ...
           TreeType);
   
           convprice(i/10+1,j*200+1) =  CbMatrix(1,1);
           stock(i/10+1,j*200+1)     =  Price;
        end    
end
    
    plot(stock, convprice);
    legend({'+0 bp'; '+50 bp'; '+100 bp'; '+150 bp'});
    title ('Effect of Spread using Trinomial tree - 200 steps')
    xlabel('Stock Price');
    ylabel('Convertible Price');
    text(50, 150, ['Coupon 4% semiannual.', sprintf('\n'), ...
         '110 Call-on-clean after two years.' sprintf('\n'), ...
         'Maturing at par in five years.'],'fontweight','Bold')

bkput

cdai