hjmsens

Instrument prices and sensitivities from Heath-Jarrow-Morton interest-rate tree

Syntax

[Delta,Gamma,Vega,Price] = hjmsens(HJMTree,InstSet)

[Delta,Gamma,Vega,Price] = hjmsens(___,Options)

Description

[Delta,Gamma,Vega,Price] = hjmsens(HJMTree,InstSet) computes instrument sensitivities and prices for instruments using an interest-rate tree created with the hjmtree function. All sensitivities are returned as dollar sensitivities. To find the per-dollar sensitivities, divide by the respective instrument price.

hjmsens handles instrument types: 'Bond', 'CashFlow', 'OptBond', 'OptEmBond', 'OptEmBond', 'OptFloat', 'OptEmFloat', 'Fixed', 'Float', 'Cap', 'Floor', 'RangeFloat', 'Swap'. See instadd for information on instrument types.

[Delta,Gamma,Vega,Price] = hjmsens(___,Options) adds an optional input argument for Options.

Examples

Compute Instrument Sensitivities Using an HJM Interest-Rate Tree

Load the tree and instruments from the deriv.mat data file. Compute Delta and Gamma for the cap and bond instruments contained in the instrument set.

load deriv.mat; 
HJMSubSet = instselect(HJMInstSet,'Type', {'Fixed', 'Cap'});  
instdisp(HJMSubSet)

Index Type  CouponRate Settle         Maturity       FixedReset Basis Principal Name     Quantity
1     Fixed 0.04       01-Jan-2000    01-Jan-2003    1          NaN   NaN       4% Fixed 80      
 
Index Type Strike Settle         Maturity       CapReset Basis Principal Name   Quantity
2     Cap  0.03   01-Jan-2000    01-Jan-2004    1        NaN   NaN       3% Cap 30      
 

Compute the Delta and Gamma for the cap and bond instruments.

[Delta, Gamma] = hjmsens(HJMTree, HJMSubSet)

Delta = 2×1

 -272.6462
  294.9700

Gamma = 2×1
103 ×

    1.0299
    6.8526

Input Arguments

HJMTree — Interest-rate tree structure

structure

Interest-rate tree structure, specified by using hjmtree.

Data Types: struct

InstSet — Instrument variable

structure

Instrument variable containing a collection of NINST instruments, specified using instadd. Instruments are categorized by type; each type can have different data fields. The stored data field is a row vector or character vector for each instrument.

Data Types: struct

Options — Derivatives pricing options structure

structure

Derivatives pricing options structure, created using derivset.

Data Types: struct

Output Arguments

Delta — Rate of change of instruments prices with respect to changes in interest rate

vector

Rate of change of instruments prices with respect to changes in the interest rate, returned as a NINST-by-1 vector of deltas. Delta is computed by finite differences in calls to hjmtree.

Note

Delta is calculated based on yield shifts of 100 basis points.

Gamma — Rate of change of instruments deltas with respect to changes in interest rate

vector

Rate of change of instruments deltas with respect to changes in the interest rate, returned as a NINST-by-1 vector of gammas. Gamma is computed by finite differences in calls to hjmtree.

Note

Gamma is calculated based on yield shifts of 100 basis points.

Vega — Rate of change of instruments prices with respect to changes in volatility

vector

Rate of change of instruments prices with respect to changes in the volatility, returned as a NINST-by-1 vector of vegas. Volatility is $$\sigma \left(t,T\right)$$ of the interest rate. Vega is computed by finite differences in calls to hjmtree. For information on the volatility process, see hjmvolspec.

Note

Vega is calculated based on 1% shift in the volatility process.

Price — Price of each instrument

vector

Price of each instrument, returned as a NINST-by-1 vector. The prices are computed by backward dynamic programming on the interest-rate tree. If an instrument cannot be priced, a NaN is returned in that entry.

Version History

Introduced before R2006a