Overview of the Finance Package - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Packages : Finance

Overview of the Finance Package

 

Calling Sequence

Description

Calling Sequence

Finance[command](arguments)

command(arguments)

Description

The Financial Modeling package is a collection of tools for mathematical finance. This package builds on the functionality available in other packages such as LinearAlgebra, Statistics, Optimization, and CurveFitting. The package supports a wide range of common tasks such as date arithmetic, cash flow analysis, option pricing, term structure analysis, and simulation.

 

For more finance examples and applications, see the Finance start page.

Cash Flow Analysis

The Financial Modeling package provides a number of tools for constructing cash flows and for performing basic sensitivity analysis.

 

AccruedAmount

-

calculate the accrued amount of a bond

BasisPointSensitivity

-

calculate the basis point sensitivity of future cash flows

CashFlows

-

return the set of cash flows for a bond or a swap

CleanPrice

-

calculate the clean price of a bond

Convexity

-

calculate the convexity of a bond or a set of cash flows

DirtyPrice

-

calculate the dirty price of a bond

Duration

-

calculate the duration of a bond or a set of cash flows

FixedRateCoupon

-

construct a fixed-rate coupon on a term structure

InArrearIndexedCoupon

-

construct an in-arrear indexed coupon

InternalRateOfReturn

-

calculate the internal rate of return of a set of cash flows or a bond

NetPresentValue

-

return the net present value of future cash flows

ParCoupon

-

construct a coupon at par on a term structure

SimpleCashFlow

-

construct a simple cash flow at a given date

UpFrontIndexedCoupon

-

construct an up-front indexed coupon on a term structure

 

More information and detailed examples can be found in Finance/Overview/CashFlowAnalysis.

Date Arithmetic

The Financial Modeling package provides various commands for performing date arithmetic. In particular, it supports over 20 different calendars and 15 day count conventions. In addition, the package provides tools for modifying existing calendars and creating non-standard calendars.

 

AddHoliday

-

add a holiday to the given calendar

AdjustDate

-

adjust a non-business day according to the given convention

AdvanceDate

-

advance a non-business day according to the given convention

Calendar

-

create a new calendar

DayCount

-

return the number of days between two dates according to a given convention

DayCounter

-

advance to the nth given day of the given month

DayOfWeek

-

 return the day of the week on which the given date falls

EvaluationDate

-

return the global evaluation date

FormatDate

-

return a string containing formatted date

IsBusinessDay

-

check if a given date is a business day according to a given calendar

IsEndOfMonth

-

check if a given date corresponds to the end of a month according to a given calendar

IsHoliday

-

check if a given date is a holiday according to a given calendar

JoinBusinessDays

-

construct new calendar by joining business days from the given two calendars

JoinHolidays

-

construct new calendar by joining holidays from the given two calendars

NextWeekday

-

advance the given date to the next given day of the week

NthWeekday

-

advance to the nth given day of the given month

ParseDate

-

parse a string containing date information

RemoveHoliday

-

remove a holiday from the given calendar

SetEvaluationDate

-

set the global evaluation date

Settings

-

return default settings

TimeGrid

-

return an object for time discretization

TodaysDate

-

return today's date according to the system clock

YearFraction

-

return the interval between two dates as a fraction of a year according to a given convention

 

More information and detailed examples can be found in Finance/Overview/Calendars and Finance/Overview/DayCounters.

Financial Instruments

The Financial Modeling package provides tools for constructing various financial instruments such as European-style and American-style options with any payoff function, bonds, as well as some interest rate instruments. In addition to this, the package provides tools for valuing these instruments and computing their market sensitivities (the Greeks). The following instruments are supported.

 

AmericanOption

-

construct an American-style option with the specified payoff function

AmericanSwaption

-

construct an American-style swaption

BermudanOption

-

construct a Bermudan-style option with the specified payoff function

BermudanSwaption

-

construct a Bermudan-style swaption

Cap

-

create new interest rate cap

Collar

-

create new interest rate collar

EuropeanOption

-

construct a European-style option with the specified payoff function

EuropeanSwaption

-

construct a European-style swaption

FixedCouponBond

-

create new fixed-coupon bond

FloatingRateBond

-

create new floating-rate bond

Floor

-

create new interest rate floor

InterestRateSwap

-

create new interest rate swap

Swap

-

create new cash-flow swap

ZeroCouponBond

-

create new zero-coupon bond

 

The following tools are available for working with the above instruments.

 

BlackPrice

-

calculate the price of an interest rate instrument using the Black model

BlackScholesCharm

-

calculate the Charm of a European-style option in the Black-Scholes model

BlackScholesColor

-

calculate the Color of a European-style option in the Black-Scholes model

BlackScholesDelta

-

calculate the Delta of a European-style option in the Black-Scholes model

BlackScholesGamma

-

calculate the Gamma of a European-style option in the Black-Scholes model

BlackScholesLambda

-

calculate the Lambda of a European-style option in the Black-Scholes model

BlackScholesPrice

-

calculate the price of a European-style option using the Black-Scholes model

BlackScholesRho

-

calculate the Rho of a European-style option in the Black-Scholes model

BlackScholesSpeed

-

calculate the Speed of a European-style option in the Black-Scholes model

BlackScholesTheta

-

calculate the Theta of a European-style option in the Black-Scholes model

BlackScholesUltima

-

calculate the Ultima of a European-style option in the Black-Scholes model

BlackScholesVanna

-

calculate the Vanna of a European-style option in the Black-Scholes model

BlackScholesVega

-

calculate the Vega of a European-style option in the Black-Scholes model

BlackScholesVera

-

calculate the Vera of a European-style option in the Black-Scholes model

BlackScholesVeta

-

calculate the Veta of a European-style option in the Black-Scholes model

BlackScholesVomma

-

calculate the Vomma of a European-style option in the Black-Scholes model

BlackScholesZomma

-

calculate the Zomma of a European-style option in the Black-Scholes model

BondOptionPrice

-

calculate the price of a discount bond option in the given affine short-rate model

CleanPrice

-

calculate the clean price of a bond

Convexity

-

calculate the convexity of a bond

DirtyPrice

-

calculate the dirty price of a bond

DiscountBondPrice

-

calculate a discount bond price

Duration

-

calculate the duration of a bond

ImpliedVolatility

-

calculate the implied volatility of a European-style option in the Black-Scholes model

ImpliedVolatilitySurface

-

construct a volatility term structure

LatticePrice

-

calculate the price of a financial instrument using a binomial or a trinomial tree

LocalVolatility

-

calculate the local volatility of a European-style option

LocalVolatilitySurface

-

create new local volatility term structure

Schedule

-

define a new payment schedule

YieldFromCleanPrice

-

calculate the yield of a bond using its clean price

YieldFromDirtyPrice

-

calculate the yield of a bond using its dirty price

 

More information and detailed examples can be found in Finance/Examples/EuropeanOptions, and Finance/Examples/AsianOptions.

Interest Rates

The Finance package also provides tools for creating and manipulating term structures of interest rates as well as volatility term structures. Here is the list of relevant commands:

 

BenchmarkRate

-

calculate benchmark rate based on a specified calendar

CompoundFactor

-

return a compound factor for the specified date or time

DiscountCurve

-

construct a yield curve based on known discount rates

DiscountFactor

-

return a discount factor for the specified date or time

EquivalentRate

-

calculate equivalent interest rate

FairRate

-

return the fair rate of an interest rate swap

FairSpread

-

return the fair spread of an interest rate swap

ForwardRate

-

compute forward rates based on a given term structure

ForwardCurve

-

construct a yield curve based on known forward rates

ImpliedRate

-

calculate interest rate implied by a given compound factor

LoadHistory

-

load historic date for a given benchmark rate

ParRate

-

compute par rates based on a given term structure

ZeroCurve

-

construct a yield curve based on known zero rates

ZeroRate

-

compute zero rates based on a given term structure

 

More information and detailed examples can be found in Finance/Overview/TermStructures.

Lattice Methods

The Financial Modeling package also provides tools for constructing binomial and trinomial trees.

 

BinomialTree

-

construct a recombining binomial tree data structure

BlackScholesBinomialTree

-

create a recombining binomial tree for a Black-Scholes process

BlackScholesTrinomialTree

-

create a recombining trinomial tree for a Black-Scholes process

ImpliedBinomialTree

-

construct an implied Black-Scholes binomial tree

ImpliedTrinomialTree

-

construct an implied Black-Scholes trinomial tree

ShortRateTree

-

construct a trinomial tree for a short-rate process

TreePlot

-

plot a binomial or trinomial tree

TrinomialTree

-

construct a mutable recombining tree data structure

 

The following commands can be used to inspect/manipulate a tree data structure.

 

GetDescendants

-

return descendants for a node of a binomial or trinomial tree

GetLocalVolatility

-

return the local volatility node of a Black-Scholes binomial or trinomial tree

GetProbabilities

-

return probabilities for a node of a binomial or trinomial tree

GetSize

-

get the size of a binomial/trinomial tree at the given level

GetUnderlying

-

return the value of the underlying for a node of a binomial or trinomial tree

SetProbabilities

-

set probabilities for a node of a binomial or trinomial tree

SetUnderlying

-

set the value of the underlying for a node of a binomial or trinomial tree

 

More information and detailed examples can be found in Finance/Overview/LatticeMethods.

Personal Finance

amortization

-amortization table for a loan

annuity

-present value of an annuity

blackscholes

-present value of a call option

cashflows

-present value of a list of cash flows

effectiverate

-convert a stated rate to the effective rate

futurevalue

-future value of an amount

growingannuity

-present value of a growing annuity

growingperpetuity

-present value of a growing perpetuity

levelcoupon

-present value of a level coupon bond

perpetuity

-present value of a perpetuity

presentvalue

-present value of an amount

yieldtomaturity

-yield to maturity of a level coupon bond

 

More information and detailed examples can be found in the Personal Finance example worksheet.

Short Rate Models

The Financial Modeling package provides the following short rate models.

 

CoxIngersollRossModel

-

Cox-Ingersoll-Ross interest rate model

HullWhiteModel

-

Hull-White interest rate model

VasicekModel

-

Vasicek interest rate model

 

Stochastic Processes

The Financial Modeling package supports a wide range of stochastic processes used in Financial Engineering. This includes processes for modeling equity prices, mean-reverting processes, pure jump processes, jump diffusions as well as multivariate Ito processes. In addition, the package provides tools for building more complicated processes from simple ones. Below is the list of supported processes:

 

BlackScholesProcess

-

Black-Scholes process

BrownianMotion

-

uni- or multi-variate Brownian motion

CEVProcess

-

constant elasticity of variance (CEV) process

DeterministicProcess

-

deterministic time-dependent process

DynamicPortfolio

-

a portfolio of stochastic processes which can be dynamically rebalanced

MarkovChain

-

a finite state Markov chain

GammaProcess

-

gamma process

GaussMarkovProcess

-

Gaussian process for modeling short-term interest rate

GeometricBrownianMotion

-

geometric Brownian motion

HestonProcess

-

stochastic volatility process introduced by Heston

ItoDiffusion

-

general uni- or multi-variate Ito process defined by drift and diffusion

ItoProcess

-

Ito process

MertonJumpDiffusion

-

jump-diffusion process introduced by Merton

RegimeSwitchingProcess

-

stochastic process with multiple regimes

OrnsteinUhlenbeckProcess

-

Ornstein-Uhlenbeck process

PoissonProcess

-

Poisson process including the doubly-stochastic Poisson (Cox) process

ShortRateProcess

-

process that governs a short rate

SquareRootDiffusion

-

square-root diffusion

SVJJProcess

-

stochastic volatility with jumps (SVJJ) process

WienerProcess

-

uni- and multi-variate Wiener process including subordinated Wiener process

 

Here are some related commands.

 

Diffusion

-

compute the diffusion component of an Ito process

Drift

-

compute the drift component of an Ito process

ExpectedShortfall

-

calculate the expected shortfall

ExpectedValue

-

compute a Monte Carlo estimate of the specified expression

PathGenerator

-

create new path generator for the specified stochastic process

PathPlot

-

plot sample path(s) of the specified stochastic process

SamplePath

-

generate a sample path for the specified stochastic process

SampleValues

-

generate sample values for the specified stochastic process

ValueAtRisk

-

estimate value-at-risk for the specified expression

 

More information and detailed examples can be found in Finance/Overview/StochasticProcesses.

See Also

Finance start page


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam