hwvolspec

Specify Hull-White interest-rate volatility process

Syntax

VolSpec = hwvolspec(ValuationDate,VolDates,VolCurve,AlphaDates,AlphaCurve)

VolSpec = hwvolspec(___,InterpMethod)

Description

VolSpec = hwvolspec(ValuationDate,VolDates,VolCurve,AlphaDates,AlphaCurve) creates a structure specifying the volatility for hwtree.

The volatility process is such that the variance of r(t + dt) - r(t) is defined as follows: V = (Volatility.^2 .* (1 - exp(-2*Alpha .* dt))) ./ (2 * Alpha). For more information on using Hull-White interest rate trees, see Hull-White (HW) and Black-Karasinski (BK) Modeling.

VolSpec = hwvolspec(___,InterpMethod) adds the optional argument InterpMethod.

Examples

Create a Structure Specifying the Volatility for hwtree

This example shows how to create a Hull-White volatility specification (VolSpec) using the following data.

ValuationDate = '01-01-2004';
StartDate = ValuationDate;
VolDates = ['12-31-2004'; '12-31-2005'; '12-31-2006'; 
'12-31-2007'];
VolCurve = 0.01;
AlphaDates = '01-01-2008';
AlphaCurve = 0.1;

HWVolSpec = hwvolspec(ValuationDate, VolDates, VolCurve,...  
AlphaDates, AlphaCurve)

HWVolSpec = struct with fields:
             FinObj: 'HWVolSpec'
      ValuationDate: 731947
           VolDates: [4x1 double]
           VolCurve: [4x1 double]
         AlphaCurve: 0.1000
         AlphaDates: 733408
    VolInterpMethod: 'linear'

Input Arguments

ValuationDate — Observation date of the investment horizon

datetime scalar | string scalar | date character vector

Observation date of the investment horizon, specified as a scalar datetime, string, or data character vector.

To support existing code, hwvolspec also accepts serial date numbers as inputs, but they are not recommended.

VolDates — Number of points of yield volatility end dates

datetime array | string array | date character vector

Number of points of yield volatility end dates, specified as a NPOINTS-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, hwvolspec also accepts serial date numbers as inputs, but they are not recommended.

VolCurve — Yield volatility values

decimal

Yield volatility values, specified as a NPOINTS-by-1 vector of decimal values. The term structure of VolCurve is the yield volatility represented by the value of the volatility of the yield from time t = 0 to time t + i, where i is any point within the volatility curve.

Note

The number of points in VolCurve and AlphaCurve do not have to be the same.

Data Types: double

AlphaDates — Mean reversion end dates

datetime array | string array | date character vector

Mean reversion end dates, specified as a NPOINTS-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, hwvolspec also accepts serial date numbers as inputs, but they are not recommended.

AlphaCurve — Positive mean reversion values

positive decimal

Positive mean reversion values, specified as a NPOINTS-by-1 vector of positive decimal values.

Note

The number of points in VolCurve and AlphaCurve do not have to be the same.

Data Types: double

InterpMethod — Interpolation method

'linear' (default) | character vector with values supported by interp1

(Optional) Interpolation method, specified as a character vector with values supported by interp1.

Data Types: char

Output Arguments

VolSpec — Specification for the volatility model for hwtree

structure

Structure specifying the volatility model for hwtree.

Version History

Introduced before R2006a

R2022b: Serial date numbers not recommended

Although hwvolspec supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.