Contents

hjmsens

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

Syntax

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

Arguments

HJMTree

Heath-Jarrow-Morton tree sampling a forward-rate process. See hjmtree for information on creating HJMTree.

InstSet

Variable containing a collection of instruments. Instruments are categorized by type. Each type can have different data fields. The stored data field is a row vector or string for each instrument.

Options

(Optional) Derivatives pricing options structure created with derivset.

Description

[Delta, Gamma, Vega, Price] = hjmsens(HJMTree, InstSet,
Options)
computes instrument sensitivities and prices for instruments using an interest-rate tree created with hjmtree. NINST instruments from a financial instrument variable, InstSet, are priced. 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 is an NINST-by-1 vector of deltas, representing the rate of change of instrument prices with respect to changes in the interest rate. Delta is computed by finite differences in calls to hjmtree. See hjmtree for information on the observed yield curve.

Gamma is an NINST-by-1 vector of gammas, representing the rate of change of instrument deltas with respect to the changes in the interest rate. Gamma is computed by finite differences in calls to hjmtree.

Vega is an NINST-by-1 vector of vegas, representing the rate of change of instrument prices with respect to the changes in the volatility σ(t,T). Vega is computed by finite differences in calls to hjmtree. See hjmvolspec for information on the volatility process.

    Note   All sensitivities are returned as dollar sensitivities. To find the per-dollar sensitivities, divide by the respective instrument price.

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

Delta and Gamma are calculated based on yield shifts of 100 basis points. Vega is calculated based on a 1% shift in the volatility process.

Examples

expand all

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', {'Bond', 'Cap'});
instdisp(HJMSubSet)
Index Type CouponRate Settle         Maturity       Period Basis EndMonthRule IssueDate FirstCouponDate LastCouponDate StartDate Face Name    Quantity
1     Bond 0.04       01-Jan-2000    01-Jan-2003    1      NaN   NaN          NaN       NaN             NaN            NaN       NaN  4% bond 100     
2     Bond 0.04       01-Jan-2000    01-Jan-2004    2      NaN   NaN          NaN       NaN             NaN            NaN       NaN  4% bond  50     
 
Index Type Strike Settle         Maturity       CapReset Basis Principal Name   Quantity
3     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)
Warning: Not all cash flows are aligned with the tree. Result will be
approximated. 

Delta =

 -272.6462
 -347.4315
  294.9700


Gamma =

   1.0e+03 *

    1.0299
    1.6227
    6.8526

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