bksens

Instrument prices and sensitivities from Black-Karasinski interest-rate tree

Syntax

[Delta,Gamma,Vega,Price] = bktsens(BKTree,InstSet)

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

Description

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

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

Examples

Compute Instrument Sensitivities and Prices for Cap and Bond Instruments

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

load deriv.mat; 
BKSubSet = instselect(BKInstSet,'Type', {'Bond', 'Cap'}); 

instdisp(BKSubSet)

Index Type CouponRate Settle         Maturity       Period Basis EndMonthRule IssueDate FirstCouponDate LastCouponDate StartDate Face Name    Quantity
1     Bond 0.03       01-Jan-2004    01-Jan-2007    1      0     1            NaN       NaN             NaN            NaN       100  3% bond 20      
2     Bond 0.03       01-Jan-2004    01-Jan-2008    1      0     1            NaN       NaN             NaN            NaN       100  3% bond 15      
 
Index Type Strike Settle         Maturity       CapReset Basis Principal Name   Quantity
3     Cap  0.04   01-Jan-2004    01-Jan-2008    1        0     100       4% Cap 10      
 

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

[Delta, Gamma] = bksens(BKTree, BKSubSet)

Delta = 3×1

 -285.7151
 -365.7048
  189.5319

Gamma = 3×1
103 ×

    0.8456
    1.4345
    6.9999

Input Arguments

BKTree — Interest-rate tree structure

structure

Interest-rate tree structure, specified by using bktree.

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 bktree.

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 bktree.

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 bktree. For information on the volatility process, see bkvolspec.

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