hjmvolspec

Specify Heath-Jarrow-Morton interest-rate volatility process

Syntax

VolSpec = hjmvolspec(Factor,Sigma_0)

VolSpec = hjmvolspec(Factor,CurveVol,CurveTerm)

VolSpec = hjmvolspec(Factor,Sigma_0,Lambda)

VolSpec = hjmvolspec(Factor,Sigma_0,CurveDecay,CurveTerm)

VolSpec = hjmvolspec(Factor,CurveProp,CurveTerm,MaxSpot)

Description

VolSpec = hjmvolspec(Factor,Sigma_0) creates a Constant volatility (Ho-Lee) structure for hjmtree by specifying the Factor as 'Constant'.

VolSpec = hjmvolspec(Factor,CurveVol,CurveTerm) creates a Stationary volatility structure for hjmtree by specifying the Factor as 'Stationary'.

VolSpec = hjmvolspec(Factor,Sigma_0,Lambda) creates an Exponential volatility structure for hjmtree by specifying the Factor as 'Exponential'.

VolSpec = hjmvolspec(Factor,Sigma_0,CurveDecay,CurveTerm) creates a Vasicek, Hull-White volatility structure for hjmtree by specifying the Factor as 'Vasicek'.

VolSpec = hjmvolspec(Factor,CurveProp,CurveTerm,MaxSpot) creates a Nearly proportional stationary volatility structure for hjmtree by specifying the Factor as 'Proportional'.

Examples

Compute the VolSpec Structure to Specify a Proportional Volatility Model for HJMTree

This example shows how to compute the VolSpec structure to specify the volatility model for hjmtree when volatility is single-factor proportional.

CurveProp = [0.11765; 0.08825; 0.06865];
CurveTerm = [1; 2; 3];
VolSpec = hjmvolspec('Proportional', CurveProp, CurveTerm, 1e6)

VolSpec = struct with fields:
          FinObj: 'HJMVolSpec'
    FactorModels: {'Proportional'}
      FactorArgs: {{1x3 cell}}
      SigmaShift: 0
      NumFactors: 1
       NumBranch: 2
         PBranch: [0.5000 0.5000]
     Fact2Branch: [-1 1]

Compute the VolSpec Structure to Specify an Exponential Volatility Model for HJMTree

This example shows how to compute the VolSpec structure to specify the volatility model for hjmtree when volatility is two-factor exponential and constant.

VolSpec = hjmvolspec('Exponential', 0.1, 1, 'Constant', 0.2)

VolSpec = struct with fields:
          FinObj: 'HJMVolSpec'
    FactorModels: {'Exponential'  'Constant'}
      FactorArgs: {{1x2 cell}  {1x1 cell}}
      SigmaShift: 0
      NumFactors: 2
       NumBranch: 3
         PBranch: [0.2500 0.2500 0.5000]
     Fact2Branch: [2x3 double]

Input Arguments

Factor — Volatility factor

character vector with value of 'Constant', 'Stationary', 'Exponential', 'Vasicek', or 'Proportional'

Volatility factor, specified as a character vector with one of the following values:

• 'Constant'

  $$\sigma \left(t,T\right)$$ = Sigma_0

• 'Stationary'

  $$\sigma \left(t,T\right)$$ = Vol(T- t) = Vol(Term)

• 'Exponential'

  $$\sigma \left(t,T\right)$$ = Sigma_0*exp(-Lambda*(T-t))

• 'Vasicek'

  $$\sigma \left(t,T\right)$$ = Sigma_0*exp(-Decay(T-t))

• 'Proportional'

  $$\sigma \left(t,T\right)$$ = Prop(T-t)*max(SpotRate(t),MaxSpot)

Note

You can specify more than one Factor by concatenating Factor names and their associated parameters.

Data Types: char

Sigma_0 — Base volatility over a unit time

numeric

Base volatility over a unit, specified as a scalar numeric value.

Data Types: double

Lambda — Decay factor

numeric

Decay factor, specified as a scalar numeric value.

Data Types: double

CurveVol — Number of curve Vol values at sample points

numeric vector

Number of curve Vol values at sample points, specified as a NCURVES-by1 vector.

Data Types: double

CurveTerm — Number of curve Term values at sample points

numeric vector

Number of curve Term values at sample points, specified as a NCURVES-by-1 vector.

Data Types: double

CurveDecay — Number of curve Decay values at sample points

numeric vector

Number of curve Decay values at sample points, specified as a NPOINTS-by-1 vector.

Data Types: double

CurveProp — Number of curve Prop values at sample points

numeric vector

Number of curve Prop values at sample points, specified as a NCURVES-by-1 vector.

Data Types: double

MaxSpot — Maximum spot rate

numeric

Maximum spot rate, specified as a scalar numeric value.

Data Types: double

Output Arguments

VolSpec — Specification for the volatility model for bktree

structure

Structure specifying the volatility model for bktree. hjmvolspec defines an HJM forward-rate volatility process based on the specified input Factor.

More About

Volatility Process

The volatility process is $$\sigma \left(t,T\right)$$, where t is the observation time and T is the starting time of a forward rate.

In a stationary process, the volatility term is T–t. Multiple factors can be specified sequentially.

The time values T, t, and Term are in coupon interval units specified by the Compounding input of hjmtimespec. For instance if Compounding = 2, Term = 1 is a semiannual period (six months).