Documentation

Financial Instruments Toolbox Functions

Yield Curves

Bootstrap from Market Data

IRDataCurve Construct interest-rate curve object from dates and data
IRBootstrapOptions Construct specific options for bootstrapping interest-rate curve object

Estimate Model Parameters

IRFunctionCurve Construct interest-rate curve object from function handle or function and fit to market data
IRFitOptions Construct specific options for fitting interest-rate curve object

Interest-Rate Instruments

Instrument Creation

instbond Construct bond instrument
instcap Construct cap instrument
instcf Construct cash flow instrument
instcbond Construct CBond instrument for convertible bond
instfixed Construct fixed-rate instrument
instfloat Construct floating-rate instrument
instfloor Construct floor instrument
instoptbnd Construct bond option
instoptembnd Construct bond with embedded option
instoptfloat Create option instrument on floating-rate note or add instrument to current portfolio
instoptemfloat Create embedded option instrument on floating-rate note or add instrument to current portfolio
instrangefloat Construct range note instrument
instswap Construct swap instrument
instswaption Construct swaption instrument

Term Structure Definition and Analysis

date2time Time and frequency from dates
datedisp Display date entries
disc2rate Interest rates from cash flow discounting factors
intenvget Properties of interest-rate structure
intenvset Set properties of interest-rate structure
rate2disc Discount factors from interest rates
ratetimes Change time intervals defining interest-rate environment
time2date Dates from time and frequency

Price Using Term Structure

bondbyzero Price bond from set of zero curves
cfbyzero Price cash flows from set of zero curves
fixedbyzero Price fixed-rate note from set of zero curves
floatbyzero Price floating-rate note from set of zero curves
intenvprice Price instruments from set of zero curves
intenvsens Instrument price and sensitivities from set of zero curves
swapbyzero Price swap instrument from set of zero curves
floatmargin Margin measures for floating-rate bond
floatdiscmargin Discount margin for floating-rate bond

Price Using Tree Models

Heath-Jarrow-Morton Tree Setup

hjmtimespec Specify time structure for Heath-Jarrow-Morton interest-rate tree
hjmtree Construct Heath-Jarrow-Morton interest-rate tree
hjmvolspec Specify Heath-Jarrow-Morton interest-rate volatility process

Heath-Jarrow-Morton Tree Analysis

bondbyhjm Price bond from Heath-Jarrow-Morton interest-rate tree
capbyhjm Price cap instrument from Heath-Jarrow-Morton interest-rate tree
cfbyhjm Price cash flows from Heath-Jarrow-Morton interest-rate tree
fixedbyhjm Price fixed-rate note from Heath-Jarrow-Morton interest-rate tree
floatbyhjm Price floating-rate note from Heath-Jarrow-Morton interest-rate tree
floorbyhjm Price floor instrument from Heath-Jarrow-Morton interest-rate tree
hjmprice Instrument prices from Heath-Jarrow-Morton interest-rate tree
hjmsens Instrument prices and sensitivities from Heath-Jarrow-Morton interest-rate tree
mmktbyhjm Create money-market tree from Heath-Jarrow-Morton interest-rate tree
oasbyhjm Determine option adjusted spread using Heath-Jarrow-Morton model
optbndbyhjm Price bond option from Heath-Jarrow-Morton interest-rate tree
optfloatbyhjm Price options on floating-rate notes for HJM interest-rate tree
optembndbyhjm Price bonds with embedded options by Heath-Jarrow-Morton interest-rate tree
optemfloatbyhjm Price embedded option on floating-rate note HJM interest-rate tree
rangefloatbyhjm Price range floating note using Heath-Jarrow-Morton tree
swapbyhjm Price swap instrument from Heath-Jarrow-Morton interest-rate tree
swaptionbyhjm Price swaption from Heath-Jarrow-Morton interest-rate tree
derivget Get derivatives pricing options
derivset Set or modify derivatives pricing options

Black-Derman-Toy Tree Setup

bdttimespec Specify time structure for Black-Derman-Toy interest-rate tree
bdttree Construct Black-Derman-Toy interest-rate tree
bdtvolspec Specify Black-Derman-Toy interest-rate volatility process

Black-Derman-Toy Tree Analysis

bdtprice Instrument prices from Black-Derman-Toy interest-rate tree
bdtsens Instrument prices and sensitivities from Black-Derman-Toy interest-rate tree
bondbybdt Price bond from Black-Derman-Toy interest-rate tree
capbybdt Price cap instrument from Black-Derman-Toy interest-rate tree
cfbybdt Price cash flows from Black-Derman-Toy interest-rate tree
fixedbybdt Price fixed-rate note from Black-Derman-Toy interest-rate tree
floatbybdt Price floating-rate note from Black-Derman-Toy interest-rate tree
floorbybdt Price floor instrument from Black-Derman-Toy interest-rate tree
mmktbybdt Create money-market tree from Black-Derman-Toy interest-rate tree
oasbybdt Determine option adjusted spread using Black-Derman-Toy model
optbndbybdt Price bond option from Black-Derman-Toy interest-rate tree
optfloatbybdt Price options on floating-rate notes for BDT interest-rate tree
optembndbybdt Price bonds with embedded options by Black-Derman-Toy interest-rate tree
optemfloatbybdt Price embedded option on floating-rate note BDT interest-rate tree
rangefloatbybdt Price range floating note using Black-Derman-Toy tree
swapbybdt Price swap instrument from Black-Derman-Toy interest-rate tree
swaptionbybdt Price swaption from Black-Derman-Toy interest-rate tree
derivget Get derivatives pricing options
derivset Set or modify derivatives pricing options

Hull-White Tree Setup

hwtimespec Specify time structure for Hull-White interest-rate tree
hwtree Construct Hull-White interest-rate tree
hwvolspec Specify Hull-White interest-rate volatility process

Hull-White Tree Analysis

bondbyhw Price bond from Hull-White interest-rate tree
capbyhw Price cap instrument from Hull-White interest-rate tree
cfbyhw Price cash flows from Hull-White interest-rate tree
fixedbyhw Price fixed-rate note from Hull-White interest-rate tree
floatbyhw Price floating-rate note from Hull-White interest-rate tree
floorbyhw Price floor instrument from Hull-White interest-rate tree
hwcalbycap Calibrate Hull-White tree using caps
hwcalbyfloor Calibrate Hull-White tree using floors
hwprice Instrument prices from Hull-White interest-rate tree
hwsens Instrument prices and sensitivities from Hull-White interest-rate tree
oasbyhw Determine option adjusted spread using Hull-White model
optbndbyhw Price bond option from Hull-White interest-rate tree
optfloatbyhw Price options on floating-rate notes for HW interest-rate tree
optembndbyhw Price bonds with embedded options by Hull-White interest-rate tree
optemfloatbyhw Price embedded option on floating-rate note HW interest-rate tree
rangefloatbyhw Price range floating note using Hull-White tree
swapbyhw Price swap instrument from Hull-White interest-rate tree
swaptionbyhw Price swaption from Hull-White interest-rate tree

Black-Karasinski Tree Setup

bktimespec Specify time structure for Black-Karasinski tree
bktree Construct Black-Karasinski interest-rate tree
bkvolspec Specify Black-Karasinski interest-rate volatility process

Black-Karasinski Tree Analysis

bkprice Instrument prices from Black-Karasinski interest-rate tree
bksens Instrument prices and sensitivities from Black-Karasinski interest-rate tree
bondbybk Price bond from Black-Karasinski interest-rate tree
capbybk Price cap instrument from Black-Karasinski interest-rate tree
cfbybk Price cash flows from Black-Karasinski interest-rate tree
fixedbybk Price fixed-rate note from Black-Karasinski interest-rate tree
floatbybk Price floating-rate note from Black-Karasinski interest-rate tree
floorbybk Price floor instrument from Black-Karasinski interest-rate tree
oasbybk Determine option adjusted spread using Black-Karasinski model
optbndbybk Price bond option from Black-Karasinski interest-rate tree
optfloatbybk Price options on floating-rate notes for BK interest-rate tree
optembndbybk Price bonds with embedded options by Black-Karasinski interest-rate tree
optemfloatbybk Price embedded option on floating-rate note BK interest-rate tree
rangefloatbybk Price range floating note using Black-Karasinski tree
swapbybk Price swap instrument from Black-Karasinski interest-rate tree
swaptionbybk Price swaption from Black-Karasinski interest-rate tree

Tree Manipulation for Interest-Rate Instruments

bushpath Extract entries from node of bushy tree
bushshape Retrieve shape of bushy tree
cvtree Convert inverse-discount tree to interest-rate tree
mkbush Create bushy tree
mktree Create recombining binomial tree
mktrintree Create recombining trinomial tree
treepath Entries from node of recombining binomial tree
treeshape Shape of recombining binomial tree
treeviewer Tree information
trintreepath Entries from node of recombining trinomial tree
trintreeshape Shape of recombining trinomial tree

Price Using Closed-Form Solutions

Black Model

capbyblk Price caps using Black option pricing model
floorbyblk Price floors using Black option pricing model
swaptionbyblk Price European swaption instrument using Black model

SABR Model

blackvolbysabr Calculate implied Black volatility using SABR model
optsensbysabr Calculate option sensitivities using SABR model

Agency OAS Models

agencyoas Determine option-adjusted spread of callable bond using Agency OAS model
agencyprice Price callable bond using Agency OAS model

Bond Futures

bndfutimprepo Implied repo rates for bond future given price
bndfutprice Price bond future given repo rates
convfactor Bond conversion factors
tfutbyprice Future prices of Treasury bonds given spot price
tfutbyyield Future prices of Treasury bonds given current yield
tfutimprepo Implied repo rates for Treasury bond future given price
tfutpricebyrepo Calculates Treasury bond futures price given the implied repo rates
tfutyieldbyrepo Calculates Treasury bond futures yield given the implied repo rates

Price Using Monte Carlo Simulation

HullWhite1F Create Hull-White one-factor model
LinearGaussian2F Create two-factor additive Gaussian interest-rate model
LiborMarketModel Create LIBOR Market Model
capbylg2f Price cap using Linear Gaussian two-factor model
floorbylg2f Price floor using Linear Gaussian two-factor model
swaptionbylg2f Price European swaption using Linear Gaussian two-factor model
blackvolbyrebonato Compute Black volatility for LIBOR Market Model using Rebonato formula
hwcalbycap Calibrate Hull-White tree using caps
hwcalbyfloor Calibrate Hull-White tree using floors

Portfolio Valuation

instadd Add types to instrument collection
instaddfield Add new instruments to instrument collection
instdelete Complement of instrument set by matching conditions
instdisp Display instruments
instfields List field names
instfind Search instruments for matching conditions
instget Data from instrument variable
instgetcell Data and context from instrument variable
instlength Count instruments
instselect Create instrument subset by matching conditions
instsetfield Add or reset data for existing instruments
insttypes List types
intenvset Set properties of interest-rate structure
hedgeopt Allocate optimal hedge for target costs or sensitivities
hedgeslf Self-financing hedge

Equity Derivatives

Instrument Creation

instasian Construct Asian option
instbarrier Construct barrier option
instcbond Construct CBond instrument for convertible bond
instcompound Construct compound option
instlookback Construct lookback option
instoptstock Construct stock option

Price Using Tree Models

Cox-Ross-Rubinstein Tree Setup

crrtimespec Specify time structure for Cox-Ross-Rubinstein tree
crrtree Construct Cox-Ross-Rubinstein stock tree
stockspec Create stock structure

Cox-Ross-Rubinstein Tree Analysis

asianbycrr Price Asian option from Cox-Ross-Rubinstein binomial tree
barrierbycrr Price barrier option from Cox-Ross-Rubinstein binomial tree
cbondbycrr Price convertible bonds from CRR binomial tree
compoundbycrr Price compound option from Cox-Ross-Rubinstein binomial tree
crrprice Instrument prices from Cox-Ross-Rubinstein tree
crrsens Instrument prices and sensitivities from Cox-Ross-Rubinstein tree
lookbackbycrr Price lookback option from Cox-Ross-Rubinstein tree
optstockbycrr Price stock option from Cox-Ross-Rubinstein tree
derivget Get derivatives pricing options
derivset Set or modify derivatives pricing options

Equal Probabilities Binomial Tree Setup

eqptimespec Specify time structure for Equal Probabilities binomial tree
eqptree Construct Equal Probabilities stock tree
stockspec Create stock structure

Equal Probabilities Binomial Tree Analysis

asianbyeqp Price Asian option from Equal Probabilities binomial tree
barrierbyeqp Price barrier option from Equal Probabilities binomial tree
cbondbyeqp Price convertible bonds from EQP binomial tree
compoundbyeqp Price compound option from Equal Probabilities binomial tree
eqpprice Instrument prices from Equal Probabilities binomial tree
eqpsens Instrument prices and sensitivities from Equal Probabilities binomial tree
lookbackbyeqp Price lookback option from Equal Probabilities binomial tree
optstockbyeqp Price stock option from Equal Probabilities binomial tree
derivget Get derivatives pricing options
derivset Set or modify derivatives pricing options

Leisen-Reimer Tree Setup

lrtimespec Specify time structure for Leisen-Reimer binomial tree
lrtree Build Leisen-Reimer stock tree
stockspec Create stock structure

Leisen-Reimer Tree Analysis

optstockbylr Price options on stocks using Leisen-Reimer binomial tree model
optstocksensbylr Determine option prices and sensitivities using Leisen-Reimer binomial tree model

Implied Trinomial Tree Setup

itttimespec Specify time structure using implied trinomial tree (ITT)
itttree Build implied trinomial stock tree
stockoptspec Specify European stock option structure

Implied Trinomial Tree Analysis

asianbyitt Price Asian options using implied trinomial tree (ITT)
barrierbyitt Price barrier options using implied trinomial tree (ITT)
compoundbyitt Price compound options using implied trinomial tree (ITT)
ittprice Price instruments using implied trinomial tree (ITT)
ittsens Instrument sensitivities and prices using implied trinomial tree (ITT)
lookbackbyitt Price lookback option using implied trinomial tree (ITT)
optstockbyitt Price options on stocks using implied trinomial tree (ITT)
derivget Get derivatives pricing options
derivset Set or modify derivatives pricing options

Tree Manipulation for Equity Instruments

bushpath Extract entries from node of bushy tree
bushshape Retrieve shape of bushy tree
cvtree Convert inverse-discount tree to interest-rate tree
mkbush Create bushy tree
mktree Create recombining binomial tree
mktrintree Create recombining trinomial tree
treepath Entries from node of recombining binomial tree
treeshape Shape of recombining binomial tree
treeviewer Tree information
trintreepath Entries from node of recombining trinomial tree
trintreeshape Shape of recombining trinomial tree

Price Using Closed-Form Solutions

Black-Scholes Model

assetbybls Determine price of asset-or-nothing digital options using Black-Scholes model
assetsensbybls Determine price and sensitivities of asset-or-nothing digital options using Black-Scholes model
cashbybls Determine price of cash-or-nothing digital options using Black-Scholes model
cashsensbybls Determine price and sensitivities of cash-or-nothing digital options using Black-Scholes model
chooserbybls Price European simple chooser options using Black-Scholes model
gapbybls Determine price of gap digital options using Black-Scholes model
gapsensbybls Determine price and sensitivities of gap digital options using Black-Scholes model
impvbybls Determine implied volatility using Black-Scholes option pricing model
optstockbybls Price options using Black-Scholes option pricing model
optstocksensbybls Determine option prices and sensitivities using Black-Scholes option pricing model
supersharebybls Calculate price of supershare digital options using Black-Scholes model
supersharesensbybls Calculate price and sensitivities of supershare digital options using Black-Scholes model

Black Model

impvbyblk Determine implied volatility using Black option pricing model
optstockbyblk Price options on futures and forwards using Black option pricing model
optstocksensbyblk Determine option prices and sensitivities on futures and forwards using Black pricing model

Roll-Geske-Whaley Model

impvbyrgw Determine implied volatility using Roll-Geske-Whaley option pricing model for American call option
optstockbyrgw Determine American call option prices using Roll-Geske-Whaley option pricing model
optstocksensbyrgw Determine American call option prices and sensitivities using Roll-Geske-Whaley option pricing model

Bjerksund-Stensland Model

impvbybjs Determine implied volatility using Bjerksund-Stensland 2002 option pricing model
optstockbybjs Price American options using Bjerksund-Stensland 2002 option pricing model
optstocksensbybjs Determine American option prices and sensitivities using Bjerksund-Stensland 2002 option pricing model
spreadbybjs Price European spread options using Bjerksund-Stensland pricing model
spreadsensbybjs Calculate European spread option prices and sensitivities using Bjerksund-Stensland pricing model

Nengjiu Ju Model

basketbyju Price European basket options using Nengjiu Ju approximation model
basketsensbyju Determine European basket options price and sensitivities using Nengjiu Ju approximation model
basketstockspec Specify basket stock structure using Longstaff-Schwartz model

Stulz Model

maxassetbystulz Determine European rainbow option price on maximum of two risky assets using Stulz option pricing model
maxassetsensbystulz Determine European rainbow option prices and sensitivities on maximum of two risky assets using Stulz pricing model
minassetbystulz Determine European rainbow option prices on minimum of two risky assets using Stulz option pricing model
minassetsensbystulz Determine European rainbow option prices and sensitivities on minimum of two risky assets using Stulz pricing model

Kirk Model

spreadbykirk Price European spread options using Kirk pricing model
spreadsensbykirk Calculate European spread option prices and sensitivities using Kirk pricing model

Kemna Vorst Model

asianbykv Prices European geometric Asian options using Kemna-Vorst model
asiansensbykv Calculate prices and sensitivities of European geometric Asian options using Kemna-Vorst model

Levy Model

asianbylevy Price of European arithmetic Asian options using Levy model
asiansensbylevy Calculate prices and sensitivities of European arithmetic Asian options using Levy model

Conze-Viswanathan and Goldman-Sosin-Gatto Models

lookbackbycvgsg Calculate prices of European lookback options using Conze-Viswanathan and Goldman-Sosin-Gatto models
lookbacksensbycvgsg Calculate prices and sensitivities of European lookback options using Conze-Viswanathan and Goldman-Sosin-Gatto models

Price Using Monte Carlo Simulation

basketbyls Price basket options using Longstaff-Schwartz model
basketsensbyls Determine price and sensitivities for basket options using Longstaff-Schwartz model
basketstockspec Specify basket stock structure using Longstaff-Schwartz model
asianbyls Price European or American Asian option using Longstaff-Schwartz model
asiansensbyls Calculate European or American Asian option prices and sensitivities using Longstaff-Schwartz model
lookbackbyls Calculate prices of lookback options using Longstaff-Schwartz model
lookbacksensbyls Calculate prices and sensitivities of lookback options using Longstaff-Schwartz model
spreadbyls Price European or American spread options using Monte Carlo simulations
spreadsensbyls Calculate price and sensitivities for European or American spread options using Monte Carlo simulations
optstockbyls Price European, Bermudan, or American vanilla options using Longstaff-Schwartz model
optstocksensbyls Calculate European, Bermudan, or American vanilla option prices and sensitivities using Longstaff-Schwartz model
optpricebysim Price option given simulated underlying values

Portfolio Valuation

instadd Add types to instrument collection
instaddfield Add new instruments to instrument collection
instdelete Complement of instrument set by matching conditions
instdisp Display instruments
instfields List field names
instfind Search instruments for matching conditions
instget Data from instrument variable
instgetcell Data and context from instrument variable
instlength Count instruments
instselect Create instrument subset by matching conditions
instsetfield Add or reset data for existing instruments
insttypes List types
stockspec Create stock structure
intenvset Set properties of interest-rate structure
basketstockspec Specify basket stock structure using Longstaff-Schwartz model
hedgeopt Allocate optimal hedge for target costs or sensitivities
hedgeslf Self-financing hedge

Energy Derivatives

Price Using Monte Carlo Simulation

spreadbyls Price European or American spread options using Monte Carlo simulations
spreadsensbyls Calculate price and sensitivities for European or American spread options using Monte Carlo simulations
asianbyls Price European or American Asian option using Longstaff-Schwartz model
asiansensbyls Calculate European or American Asian option prices and sensitivities using Longstaff-Schwartz model
lookbackbyls Calculate prices of lookback options using Longstaff-Schwartz model
lookbacksensbyls Calculate prices and sensitivities of lookback options using Longstaff-Schwartz model
optstockbyls Price European, Bermudan, or American vanilla options using Longstaff-Schwartz model
optstocksensbyls Calculate European, Bermudan, or American vanilla option prices and sensitivities using Longstaff-Schwartz model
optpricebysim Price option given simulated underlying values

Price Using Closed-Form Solutions

spreadbykirk Price European spread options using Kirk pricing model
spreadsensbykirk Calculate European spread option prices and sensitivities using Kirk pricing model
spreadbybjs Price European spread options using Bjerksund-Stensland pricing model
spreadsensbybjs Calculate European spread option prices and sensitivities using Bjerksund-Stensland pricing model
asianbykv Prices European geometric Asian options using Kemna-Vorst model
asiansensbykv Calculate prices and sensitivities of European geometric Asian options using Kemna-Vorst model
asianbylevy Price of European arithmetic Asian options using Levy model
asiansensbylevy Calculate prices and sensitivities of European arithmetic Asian options using Levy model
lookbackbycvgsg Calculate prices of European lookback options using Conze-Viswanathan and Goldman-Sosin-Gatto models
lookbacksensbycvgsg Calculate prices and sensitivities of European lookback options using Conze-Viswanathan and Goldman-Sosin-Gatto models
optstockbyblk Price options on futures and forwards using Black option pricing model
optstocksensbyblk Determine option prices and sensitivities on futures and forwards using Black pricing model

Price Using Finite Differences

spreadbyfd Price European or American spread options using finite difference method
spreadsensbyfd Calculate price and sensitivities of European or American spread options using finite difference method

Credit Derivatives

Credit Default Swaps

cdsbootstrap Bootstrap default probability curve from credit default swap market quotes
cdsprice Determine price for credit default swap
cdsspread Determine spread of credit default swap
cdsrpv01 Compute risky present value of a basis point for credit default swap

Credit Default Swap Options

cdsoptprice Price payer and receiver credit default swap options
cdsrpv01 Compute risky present value of a basis point for credit default swap

Counterparty Credit Risk

creditexposures Compute credit exposures from contract values
exposureprofiles Compute exposure profiles from credit exposures

Mortgage-Backed Securities

Mortgage Pass-Through

mbscfamounts Cash flow and time mapping for mortgage pool
mbsconvp Convexity of mortgage pool given price
mbsconvy Convexity of mortgage pool given yield
mbsdurp Duration of mortgage pool given price
mbsdury Duration of mortgage pool given yield
mbsnoprepay End-of-month mortgage cash flows and balances without prepayment
mbspassthrough Mortgage pool cash flows and balances with prepayment
mbsprice Mortgage-backed security price given yield
mbswal Weighted average life of mortgage pool
mbsyield Mortgage-backed security yield given price
mbsprice2speed Implied PSA prepayment speeds given price
mbsyield2speed Implied PSA prepayment speeds given yield
psaspeed2default Benchmark default
psaspeed2rate Single monthly mortality rate given PSA speed
mbsoas2price Price given option-adjusted spread
mbsoas2yield Yield given option-adjusted spread
mbsprice2oas Option-adjusted spread given price
mbsyield2oas Option-adjusted spread given yield

Collateralized Mortgage Obligations

cmoseqcf Generate cash flows for sequential collateralized mortgage obligation (CMO)
cmoschedcf Generate cash flows for scheduled collateralized mortgage obligation (CMO) using PAC or TAC model
cmosched Generate principal balance schedule for planned amortization class (PAC) or targeted amortization class (TAC) bond
mbscfamounts Cash flow and time mapping for mortgage pool
cfspread Compute spread over yield curve for cash flow
cfprice Compute price for cash flow given yield to maturity
cfyield Compute yield to maturity for cash flow given price

Convertible Bonds

cbprice Price convertible bond
cbondbycrr Price convertible bonds from CRR binomial tree
cbondbyeqp Price convertible bonds from EQP binomial tree
instcbond Construct CBond instrument for convertible bond
instadd Add types to instrument collection
instdisp Display instruments
eqpprice Instrument prices from Equal Probabilities binomial tree
crrsens Instrument prices and sensitivities from Cox-Ross-Rubinstein tree
eqpsens Instrument prices and sensitivities from Equal Probabilities binomial tree

Numerix Interface

numerix Create numerix object to set up Numerix CAIL environment
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