Innovative Securities & Derivatives Analysis Software for Professionals!

Derivatives Expert is a complete, well-integrated suite of functions for doing complex financial analysis and engineering with respect to many exchange and Over-The-Counter (OTC) traded securities and derivatives. Derivatives Expert fills a unique niche in the market for high-end financial analysis tools by providing financial engineers with an easy-to-use desktop environment for exploring, prototyping, and testing financial models without the programming overhead of larger, less-integrated systems. This makes Derivatives Expert an indispensable desktop tool for all serious financial analysts, brokers, traders, investment bankers, portfolio managers, treasurers, and financial consultants.

Derivatives Expert is complete.

Derivatives Expert and Mathematica combine to provide a full complement of financial analysis tools, enabling users to become productive quickly. The latest version of Derivatives Expert provides approximately 428 symbols (functions, arguments, and optionals), has been fully updated to Mathematica 4, and now includes many functions for pricing "exotic" options. Specialized packages are also included for Bonds, Mortgage Backed Obligations, Floaters, Forwards, Swaps, and Standard Options. To insure that users are supported from the very beginning, Derivatives Expert includes extensive online documentation, including background material, a user's guide, a reference manual, and detailed programming examples.

Derivatives Expert is flexible.

Building on the clean, modular design of the Mathematica programming language, Derivatives Expert provides a uniquely flexible environment for customizing functions and doing modern financial engineering. The focus in Derivatives Expert is not on single financial products but on the construction of a framework that can contain all financial instruments in a unified way. The end result is that it is very easy for users to expand the system with new functionality and support of new financial instruments.

Derivatives Expert is extensible.

As with any Mathematica application package, Derivatives Expert can be combined with other commercial packages to create a custom-designed solution to your individual problem. With Mathematica Link for Excel, for example, Derivatives Expert functionality can be incorporated into the familiar environment of Excel, and with the new Database Access Kit any ODBC-compliant database may be linked to Derivatives Expert for added data-management capabilities.

Features

Calendar Tools

This package is a very extensive calendar functions package, designed especially for financial analysis. The package can also be used in other fields of analysis. It is possible to work with normal calendar dates, holidays, workdays and most (probably all) financial day counting methods. The day counting methods are implemented in a rather general way.

The complexity of the functions in this package varies a great deal. Some are very simple, while others come in several versions with many different optional settings. All functions, however, are quite straightforward to understand and use.

Utility Tools

This package contains a number of small but helpful functions, that are normally only relevant for you if you program further using the functions of Derivatives Expert.

Discounting Tools

This package consists of functions that can calculate discount factors and compound factors in various ways (linear, exponential, linear-exponential and continuous compounding). A discount factor can be interpreted as the present value of a zero-coupon bond paying one monetary unit at the maturity date. A compound factor can be interpreted as the future value of one monetary unit placed today.

Functions include both discrete-time and continuous-time versions. Both calendar time and non-calendar time versions are available. The only difference between the non-calendar time versions and the calendar time versions is the possibility of using dates. By using dates it follows that different day counting conventions have influence on the results. This is because the day counting conventions control the period length calculation methods.

The function DiscountFactors for example takes a list of dates or a list of period lengths, for which discount factors are wanted and a term structure and returns the corresponding list of discount factors.

The discount factors are central to all asset and liability pricing. Discount factors are used in the function PresentValue, from the PricingTools.m module, for example to discount all relevant cash flows to some reference in time (e.g. today). If cash flows are not discounted they are often referred to as nominal cash flows.

Term Structure Tools

This package provides functions for calculating ordinary spot interest rates, forward interest rates according to different methods (linear, exponential, linear-exponential and continuous), estimation of zero-coupon term structures from prices and cash flows and for fitting discrete interest rates to a continuous term structure function. In addition there are different conversion functions that can handle nominal, effective, periodic and annual rates.

In order to understand instruments like forward rate agreements, money market forwards and foreign exchange forwards (see the Forwards.m package) it is necessary to know what a forward rate is. The function ToForwardRate, from the TermStructureTools.m package, is defined and calculated entirely from the knowledge of spot interest rates. Instruments which have a variable coupon, like floating rate bonds/notes (see the Floaters.m package), can also be priced using forward rates.

When analyzing portfolios incorporating different interest rate sensitive instruments, it is useful to use zero-coupon interest rates as a common yardstick for pricing the cash flows. Using the individual yields to maturity on each instrument will not provide a correct way to compare different interest rate sensitive products, unless the cash flow patterns of each instrument are very similar. The function EstimateTermStructure can calculate zero-coupon interest rates. These rates can be used to price cash flows, for example using functions from the PricingTools.m package.

Cash Flow Tools

This package includes a number of functions which are often needed in cash flow generation and pricing. A large collection of calendar functions can be utilized in this context, for example to restrict cash flow dates to business days for example. The functions can both be generated in non-calendar time and in calendar time. All in all, most functions are more general than usually seen.

Refer also to the summaries below regarding specific securities and instruments.

Pricing Tools

This package, in connection with other Derivatives Expert packages, includes functions to calculate the present value (with or without accrued interest), the theoretical price, the implicit volatility and the implicit yield on general financial contracts and a long range of specific financial securities and instruments.

Refer also to the summaries below regarding specific securities and instruments.

Static Risk Tools

This package includes tools to measure the static risks (sensitivities) of financial contracts. Static, in this sense, means "What happens when we go from state 1 to state 2 ?". Of course, the rate at which the change occurs is of great importance and must be evaluated by you.

TermStructureRisk is defined as the profit or loss on a position (an actual asset or liability holding) stemming from a shift in the term structure from state 1 to state 2. The first term structure represents the state before any change in the term structure has occured, and the second term structure represents the state after the change. TermStructureRisk is also available in a general version which takes a cash flow and two term structure functions (one for state 1 and one for state 2) as input.
Note that a term structure in Derivatives Expert is specified as a function and that the only requirement about this function is that there must be a one-to-one correspondance between domain values and function values, i.e. there is exactly one interest rate for every time to maturity.

The function Duration can be used to calculate the average time until the cash flow is received. This is the Macaulay method. Duration can also be used to calculate the term structure risk on cash flows that are not dependent on the yield level. This is the ModifiedMacaulay method. The duration is based on first partial derivatives and is therefore not always an accurate method for measuring term structure risk, also because it implicitly assumes that term structures are flat.

The function TermStructureRisk is generally a more correct way of measuring static term structure risk than Duration.

The function D is used to calculate the first and second order partial derivatives of option pricing functions.

The function Elasticity is used to calculate an option's price elasticity. Price elasticity is defined as the relative change in the option's price, caused by a relative change in one of the function's variables, e.g. the spot price of the underlying security.

Refer also to the summaries below regarding specific securities and instruments.

Bonds

This package consists of very general and flexible functions which can generate a variety of different cash flows for the bond types Annuity, Bullet, Consol, Serial and Zero (short for zero-coupon bond). The cash flow functions are: CashFlow, Repayment, OutstandingPrincipal and Coupon. Pricing and risk estimation functions are also included. These are: PresentValue, ImplicitYield, Duration and TermStructureRisk.

A PassThrough (in the MortgageBackedObligations.m package) is a convertible Annuity. A Float (from the Floaters.m package) can have any amortization pattern, for example the same patterns as Annuity, Bullet, Consol, Serial and Zero. Generally any non-convertible bond can be assembled from a number of zero-coupon bonds.

Mortgage Backed Obligations

This package consists of very general and flexible functions for calculating a variety of different cash flows, prepayment schedules, survival rates, present values and term structure risks for the instrument type PassThrough. Pass throughs are the basis for many different kinds of mortgage backed instruments, i.e. collateral mortgage obligation, principal only, interest only etc.

Note that it is possible to define an adjusteble rate mortgage backed obligation by combining a PassThrough with a Float. Refer to the package Floaters.m. Refer also to the Bonds.m package where non-convertible annuities are treated.

Floaters

This package consists of very general and flexible functions to calculate the coupons, cash flows, present values, implicit yields and term structure risks of generalized floating rate securities/instruments (Float). With these functions, a long list of optionals can be included in the calculations, namely: a reset lag, a reference interest index duration, a cap, a floor, a constant multiplied by the underlying interest rate and a fixed interest rate part (a spread). Furthermore, it is possible to have different amortization schedules on which the coupon and cash flow calculations are done.

The coupon of a floating rate instrument is variable and depends on some interest rate index. Therefore not only the price of float is a function of the interest rate index, but the coupon is also a function of the interest rate index. This is not the case with a fixed coupon rate instrument. The coupon of a "typical" floating rate instrument is positively correlated with the interest rate index and therefore a more price stable instrument than a "corresponding" fixed rate instrument.

Often floaters issued in the USA incorporate a coupon that is directly dependent on a Treasury instrument, e.g. the average of previously issued 3-month Treasury Bills plus some credit risk markup. LIBOR is another often used reference interest rate.

The amortization patterns of Annuity, Bullet, Consol, Serial and Zero of the Bonds.m package can be utilized by the Float object. In fact any (reasonable) amortization pattern can be used with the Float.

An adjustable rate mortage backed bond (ARM) is analyzed in this chapter. This is done with the PassThrough (object) from the MortgageBackedObligations.m package. The forward rate related functions in the TermStructureTools.m package are of great importance for the Floaters.m package.

Forwards

This package consists of very general and flexible functions to calculate the cash flows, present values, theoretical prices and term structure risks of generalized forward rate agreements, generalized money market forwards, foreign exchange forwards and plain forwards.

A forward contract is an obligation to make delivery (a short position) or accept delivery (a long position) of a specific underlying instrument at a place and future date - terms which are specified by the contract. A futures contract is a standardized forward contract that is exchange traded with daily regulations of profits and losses. A forward is traded Over The Counter (OTC), i.e. through a broker.

Please note that it is generally not correct to use valuation procedures meant for forward instruments on futures instruments.

Swaps

This package consists of very general and flexible functions to calculate cash flows, theoretical prices, present values and term structure risks of swaps. The functions can be used to analyze interest rate swaps and currency swaps (plain currency swaps, basis swaps and fixed swaps) that are standard swap types. It is also possible to analyze swaptions.

With Derivatives Expert it is easy to construct new complicated swaps.

Swaps enable a borrower to raise funds in the market to which he has best access, but to make interest and principal payments under the conditions (e.g. fixed or floating rate coupons) and in the currency of his preference. Swaps are useful for a number of reasons: to hedge interest rate or currency exposure, to obtain low-cost financing, to earn fees, to speculate etc.

Typical swaps are derived from bonds and/or floaters, so these instruments and the packages dealing with them, namely the Bonds.m and Floaters.m packages, must also be understood. A swaption is one of the most complex financial instruments in Derivatives Expert and is based and constructed by using elements from many of the Derivatives Expert packages/modules.

Options

This chapter contains important information about and examples of how to use those functions/components in Derivatives Expert that relate to standard American and European options in general. Specific option models are also documented in this chapter.

Black & Scholes

This chapter contains important information about and examples of how to use the Derivatives Expert functions/components that describe the Black & Scholes (1973) option pricing model, The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81 (May-June 1973), pp. 637-54.

The Black & Scholes (1973) model was a breakthrough in option pricing because it specified the option price solely as a function of known variables. The model is applicable for valuing European Call and European Put options on non-dividend paying stock. The theoretical prices, implied volatilities, elasticities and the first and second order partial derivatives of the option pricing functions with respect to each of the arguments of the option pricing function are implemented in the BlackScholes package.

Black

This chapter contains important information about and examples of how to use the Derivatives Expert functions/components that describe the Black (1976) option pricing model, The Pricing of Commodity Contracts, Journal of Financial Economics, 3 (Jan. - Mar.), pp. 167-179.

The model is applicable for valuing European call and European put options on commodity futures. The exact nature of the underlying commodity varies and may be anything from a precious metal such as gold or silver to agricultural products. The theoretical prices, implied volatilities, elasticities and the first and second order partial derivatives of the option pricing functions with respect to each of the arguments of the option pricing function are implemented in the Black76 package.

Cox, Ross & Rubinstein

This chapter contains important information about and examples of how to use the Derivatives Expert functions/components that describe the Cox, Ross & Rubinstein (1979) option pricing mode, A Simplified Approach, Journal of Financial Economics 7, pp. 229-263.

The Cox, Ross & Rubinstein (1979) was another milestone in option pricing because it made it possible to price American and European options on dividend paying instruments in a rather simple manner using only non-arbitrage arguments.

The model is a dicrete time model in contrast to the Black & Scholes model which is a continuous time model. Another important difference is that the Black & Scholes model is an analytical (exact) model while the Cox, Ross & Rubinstein (1979) model is an approximate model based on numerical methods. The Cox, Ross & Rubinstein (1979) model also shows that the option price can be interpreted as the expected discounted future value in a risk-neutral world. Risk-neutral pricing methodologies have since been refined using martingale theory (from probability theory).

In Derivatives Expert two versions from "A Simplified Approach" are implemented: they are called Binomial1 and Binomial2.

Binomial1 represents a model that converges to the Black & Scholes (1973) model when the number of trading periods equals a large positive integer. European call options can be priced with this model. It is included for illustration purposes only, because it is normally better to use the Black & Scholes model directly for pricing purposes.

Binomial2 represents a non-dividend version of the general recursive model. American call and put options and European call options can be priced in Derivatives Expert. With no dividends, a European call option and an American call option will have the same price, but this may not be the case with put options.

Binomial3 represents a dividend version of the general recursive model where also the timing of the dividends can be specified. American call and put options can be priced in Derivatives Expert. With dividends, a European option and an American option will not have the same price.

Garman & Kohlhagen

This chapter contains important information about and examples of how to use the Derivatives Expert functions/components that describe the Garman & Kohlhagen (1983) option pricing model, Foreign Currency Option Values, Journal of International Money and Finance, 2(3), pp. 231-238.

This model is applicable for valuing European call and European put options on foreign exchange. The theoretical prices, implied volatilities, elasticities and the first and second order partial derivatives of the option pricing functions with respect to each of the arguments of the option pricing function are implemented in the GarmanKohlhagen package.

Shastri & Tandon

This chapter contains important information about and examples of how to use the Derivatives Expert functions/components that describe the Shastri & Tandon (1987) option pricing model: Valuation of American Options on Foreign Currency, Journal of Banking and Finance 11 (1987), pp. 245-269.

The model is applicable for valuing European call, American call, European put and American put options on foreign exchange. Using the analytical techniques developed by Geske and Johnson (1984), The American put valued analytically, Journal of Finance 39, Dec. pp. 1511-1524, these securities are priced as a sequence of compound options. A total of nine different functions from the Shastri and Tandon (1987) formulas are provided in the ShastriTandon package. The Garman & Kohlhagen (1983) model is a special case of this model.

Barone-Adesi & Whaley

This chapter contains important information about and examples of how to use the Derivatives Expert functions/components that describe the Barone-Adesi & Whaley (1987) option pricing model, Efficient Analytic Approximation of American Option Values, The Journal of Finance, Vol. XLII, No.2, June.

This model provides approximate (not fully analytical) functions for valuing American call, European call, American put and European put options on commodities and commodity futures contracts. The method is called the quadratic approximation method. Quoting directly from the paper: "The exact nature of the underlying commodity varies, and may be anything from a precious metal such as gold or silver to a financial instrument such as a Treasury Bond, foreign currency, or a constant dividend paying stock".

The Black & Scholes (1973), Black (1976), Garman & Kohlhagen (1983) and Shastri & Tandon (1987) are all special cases of the Barone-Adesi & Whaley (1987) model, but the model is not accurate in all cases when the time to expiration of the option is more than one year. In this case e.g. the Binomial2 model can be used if the underlying instrument is appropriate.

Option Graphics

In this chapter we show examples of two- and three-dimensional graphics made with Derivatives Expert's option pricing functions and Mathematica's graphical functions. The examples are intended to show a few of the graphical capabilities.

Exotic Options 1

This notebook covers a long range of non-standard path dependent options that belong to the "exotic" options family. There are more than 40 different exotic options covered here. All the option pricing models operate in a continuous-time Black & Scholes-like environment.

Exotic Options 2

This chapter covers a long range of correlation or multiasset options. There are more than 28 different exotic options covered here. All the option pricing models operate in a continuous-time Black & Scholes-like environment.