Get the latest updates and news from FINCAD. Subscribe and never miss a post! 


Financial Architecture Series, Part 3: Payment Amounts - The Index Concept
By Russell Goyder PhD | April 4, 2013

In part 1 and part 2, I described how parties to a contract may be obliged to make payments and described the basic anatomy of a payment, but deferred the topic of exactly how the payment amount is specified, until now.

The key requirement for the definition of a payment is unambiguous determination of the amount to be paid, when required. When the payment amount is determined and when the payment is made are two distinct events, with the latter falling no earlier than the former. Indeed, a small delay is common, to accommodate the practicalities of delivery. An indicative list of those unambiguously determinable quantities which form the definition of payment amounts would include

  • equity prices,
  • equity indices,
  • interest rates,
  • whether a credit entity has defaulted, and
  • foreign exchange rates.

However, this is very far from an exhaustive list. It is these quantities which are the “underlyings” from which a derivative contract is derived and therefore is so-called. The common feature of all of these quantities is their ability to form part of the definition of a future payment in a contract written today. For each it is possible to refer to an established methodology for observing the value in the future. Sufficient detail must be included, such as the exact definition of credit default for example, and if there is an appreciable chance of an observation not being possible when required, further provision must be made for an alternative course of action.

Such details are the province of the legal counsel of each party to a contract; for our purposes is it sufficient to recognize that there is a concept, that of an Index, which can be characterized as:

  • the definition of a quantity on which a payment is contingent

It is critical to note the careful terminology in the above statement. The Index concept concerns the definition only of an underlying, not its actual value at any given time.

For example, the British Bankers’ Association provides the definition of several LIBOR rates on its web site. It is possible to read how LIBOR values are obtained (it is by topping and tailing the results of an opinion poll of 16 London banks). The same organization also documents the rules and conventions for determining the start and end dates of the borrowing period relevant to each rate, given an observation (or fixing) day. The inverse rules are also documented, showing how to determine the correct fixing date for a given borrowing period. All of this information is part of the definition of the concept of LIBOR and all of it pertains to every LIBOR rate ever observed.

The Index concept makes this subtle distinction between the definition of the value and the value itself, because its purpose is to encode the information present in the legal contract, where it is sufficient to describe how, at some future time when an observation of the underlying is required, to go about making the observation.

In my next post I'll go into how the Index concept relates to complex payoffs.

About the author
Russell Goyder PhD
Russell Goyder PhD
Director of Quantitative Research and Development | FINCAD

Russell Goyder, PhD, is the Director of Quantitative Research and Development at FINCAD. Before joining FINCAD’s quant team in 2006, he worked as a consultant at The MathWorks, solving a wide range of problems in various industries, particularly in the financial industry. In his current role, Russell manages FINCAD’s quant team and oversees the delivery of analytics functionality in FINCAD’s products, from initial research to the deployment of production code. Russell holds a PhD in Physics from the University of Cambridge.