About ...
the William Margrabe Group, Inc.

The William Margrabe Group, Inc. (WMG, Inc.; the Group), a consulting firm since 1994, provides clients with goods and services related to mathematical and statistical models for business purposes. Almost all of these business models have been economic models, of which almost all have been financial models, of which most have been models for pricing and managing the risk of derivative products (such as swaps and options), bonds, and money market instruments. The underlying risk factors have include prices of bonds, currencies, real estate, and shares; yields of money market instruments, notes, and bonds; degree-days, default risk; mortality risk; indexes of the preceding; spot, forward, and futures prices; functions of the preceding; etc.  

Mission:

The mission of the William Margrabe Group, Inc. is to help its clients obtain (build, buy, or license), document, evaluate, understand, and use financial models, algorithms, source code, applications, systems, etc.

Our services range from documenting to analyzing to reviewing to reporting. The deliverables may include English-language documents, computer code, instructional seminars, etc.

Client have included major commercial banks and investment banks, buy-side clients of such institutions, federal regulatory agencies, accounting firms, etc.

We have licensed a wide variety of financial models--mostly, prototypes--to clients.

Vision

The Group's vision is to be for firms that use financial models for sales, trading, and management of rewards and risks, what Clark Clifford was for Presidents Truman, Kennedy, and Johnson—without, of course, capping one's career by having anything to do with an analog of the Bank of Credit and Commerce International. 

About "Margrabe Option"

A "Margrabe option" is an option to exchange one asset for another. Other names for this option include "exchange option" and "swap option".

It's payoff function is , where X₁ and X₂ are the underlying asset values.

It is a simple "Rainbow option", so-called, because it can have a "spectrum" (in this case, with just two members) of underlying assets. 

About "Margrabe Model"

The "Margrabe Model" is an option pricing model that gives the value for a Margrabe option, when the two underlying asset prices are log normal random variables, the variance of the logarithm of the ratio of the underlying price variables is constant, and other "Black-Scholes-Merton" assumptions hold.

The Margrabe model is "isomorphic" to the Black-Scholes (1973), Merton (1973), Black (1976), Garman-Kohlhagen (1983), and many other option pricing models, which proved useful when Fischer Black arranged in the middle 1980s for me to fly to New York as a consultant, to work with a talented C-programmer quant in his group at Goldman Sachs to implement the Margrabe model.