floatbyzero - Price floating-rate note from set of zero curves

Syntax

[Price, PriceNoAI, OutputCashFlows, CFlowDates] = floatbyzero(RateSpec, Spread, Settle, Maturity) [Price, PriceNoAI, OutputCashFlows, CFlowDates] = floatbyzero(RateSpec, Spread, Settle, Maturity, Reset, Basis, Principal, EndMonthRule, LatestFloatingRate, ForwardRateSpec) [Price PriceNoAI, OutputCashFlows, CFlowDates] = floatbyzero(RateSpec, Spread, Settle, Maturity, Name, Value)

Description

[Price, PriceNoAI, OutputCashFlows, CFlowDates] = floatbyzero(RateSpec, Spread, Settle, Maturity) computes the price of a floating-rate note from a set of zero curves.

[Price, PriceNoAI, OutputCashFlows, CFlowDates] = floatbyzero(RateSpec, Spread, Settle, Maturity,Reset, Basis, Principal, EndMonthRule, LatestFloatingRate, ForwardRateSpec) computes the price of a floating-rate note from a set of zero curves using optional input arguments.

[Price PriceNoAI, OutputCashFlows, CFlowDates] = floatbyzero(RateSpec, Spread, Settle, Maturity,Name, Value) computes the price of a floating-rate note from a set of zero curves with additional options specified by one or more Name, Value pair arguments.

Input Arguments

`RateSpec`	Structure containing the properties of an interest-rate structure. See `intenvset` for information on creating `RateSpec`.
`Spread`	Number of basis points over the reference rate.
`Settle`	Settlement date. `Settle` must be earlier than `Maturity`.
`Maturity`	Maturity date.

Ordered Input or Name-Value Pair Arguments

Enter the following optional inputs using an ordered syntax or as name-value pair arguments. You cannot mix ordered syntax with name-value pair arguments.

`Reset`	`NINST`-by-`1` vector representing the frequency of payments per year. Default: `1`
`Basis`	Day-count basis of the instrument. A vector of integers. 0 = actual/actual 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) 13 = BUS/252 For more information, see basis. Default: `0` (actual/actual)
`Principal`	`NINST`-by-`1` vector of notional principal amounts or `NINST`-by-`1` cell array. For the latter case, each element of the cell array is a `NumDates`-by-`2` matrix where the first column is dates and the second column is associated principal amount. The date indicates the last day that the principal value is valid. Default: `100`
`EndMonthRule`	End-of-month rule. `NINST`-by-`1` vector. 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 coupon payment date is always the same numerical day of the month. `1` = Set rule on, meaning that a bond coupon payment date is always the last actual day of the month. Default: `1`
`LatestFloatingRate`	Rate for the next floating payment set at the last reset date. `NINST`-by-`1` of scalars. If this is not specified, the floating rate at the previous reset date must be computed from the `RateSpec`.
`ForwardRateSpec`	The `RateSpec` to be used in generating floating cash flows. If no `ForwardRateSpec` is specified then the `RateSpec` is used to generate floating cash flows.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments, where Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

AdjustCashFlowsBasis

Adjust the cash flows based on the actual period day count. NINST-by-1 of logicals.

Default: false

BusinessDayConvention

Require payment dates to be business dates. NINST-by-1 cell array with possible choices of business day convention:

actual
follow
modifiedfollow
previous
modifiedprevious

Default: actual

Holidays

Holidays used for business day convention. NHOLIDAYS-by-1 of MATLAB date numbers.

Default: If no dates are specified, holidays.m is used.

Output Arguments

Price

Number of instruments (NINST) by number of curves (NUMCURVES) matrix of floating-rate note prices. Each column arises from one of the zero curves.

PriceNoAI

NINST-by-NUMCURVES matrix of dirty bond price (clean + accrued interest). Each column arises from one of the zero curves.

OutputCashFlows

NINST-by-NUMCFS matrix of cash flows for each bond.

Note If there is more than one curve specified in the RateSpec input, then the first NCURVES rows correspond to the first bond, the second NCURVES rows correspond to the second bond, and so on.

CFlowDates

NINST-by-NUMCFS matrix of payment dates for each bond.

Examples

Price a Floating-Rate Note Using a Set of Zero Curves

Price a 20-basis point floating-rate note using a set of zero curves.

Load deriv.mat, which provides ZeroRateSpec, the interest-rate term structure, needed to price the bond.

load deriv.mat;

Define the floating-rate note using the required arguments. Other arguments use defaults.

Spread = 20;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2003';

Use floatbyzero to compute the price of the note.

Price = floatbyzero(ZeroRateSpec, Spread, Settle, Maturity)

Price =

  100.5529

Price an Amortizing Floating-Rate Note

Price an amortizing floating-rate note using the Principal input argument to define the amortization schedule.

Create the RateSpec.

Rates = [0.03583; 0.042147; 0.047345; 0.052707; 0.054302];
ValuationDate = '15-Nov-2011';
StartDates = ValuationDate;
EndDates = {'15-Nov-2012';'15-Nov-2013';'15-Nov-2014' ;'15-Nov-2015';'15-Nov-2016'};
Compounding = 1;
RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,...
'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)

RateSpec = 

           FinObj: 'RateSpec'
      Compounding: 1
             Disc: [5x1 double]
            Rates: [5x1 double]
         EndTimes: [5x1 double]
       StartTimes: [5x1 double]
         EndDates: [5x1 double]
       StartDates: 734822
    ValuationDate: 734822
            Basis: 0
     EndMonthRule: 1

Create the floating-rate instrument using the following data:

Settle ='15-Nov-2011';
Maturity = '15-Nov-2015';
Spread = 15;

Define the floating-rate note amortizing schedule.

Principal ={{'15-Nov-2012' 100;'15-Nov-2013' 70;'15-Nov-2014' 40;'15-Nov-2015' 10}};

Compute the price of the amortizing floating-rate note.

Price  = floatbyzero(RateSpec, Spread, Settle, Maturity, 'Principal', Principal)

Price =

  100.3059

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