bdtsens

Instrument prices and sensitivities from Black-Derman-Toy interest-rate tree

Syntax

[Delta,Gamma,Vega,Price] = bdtsens(BDTTree,InstSet)

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

Description

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

bdtsens 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] = bdtsens(___,Options) adds an optional input argument for Options.

Examples

Compute Instrument Sensitivities and Prices for Cap and Float Instruments

Load the tree and instruments from the deriv.mat data file.

load deriv.mat; 
BDTSubSet = instselect(BDTInstSet,'Type', {'Float', 'Cap'});  
 
instdisp(BDTSubSet)

Index Type  Spread Settle         Maturity       FloatReset Basis Principal Name       Quantity
1     Float 20     01-Jan-2000    01-Jan-2003    1          NaN   NaN       20BP Float 8       
 
Index Type Strike Settle         Maturity       CapReset Basis Principal Name    Quantity
2     Cap  0.15   01-Jan-2000    01-Jan-2004    1        NaN   NaN       15% Cap 30      
 

Compute Delta and Gamma for the cap and float instruments contained in the instrument set.

[Delta, Gamma] = bdtsens(BDTTree, BDTSubSet)

Delta = 2×1

   -0.8392
   63.8102

Gamma = 2×1
103 ×

    0.0025
    1.8535

Input Arguments

BDTTree — Interest-rate tree structure

structure

Interest-rate tree structure, specified by using bdttree.

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

(Optional) 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 bdttree.

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 bdttree.

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 bdttree. For information on the volatility process, see bdtvolspec.

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