hjmsens

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

Description

example

[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.

example

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

Examples

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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.

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

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Interest-rate tree structure, specified by using hjmtree.

Data Types: struct

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

Derivatives pricing options structure, created using derivset.

Data Types: struct

Output Arguments

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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.

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.

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 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.

Introduced before R2006a