Composing contracts

Abstract

Financial and insurance contracts do not sound like promising territory for functional programming and formal semantics, but in fact we have discovered that insights from programming languages bear directly on the complex subject of describing and valuing a large class of contracts.We introduce a combinator library that allows us to describe such contracts precisely, and a compositional denotational semantics that says what such contracts are worth. We sketch an implementation of our combinator library in Haskell. Interestingly, lazy evaluation plays a crucial role.

Putting Gradual Types to Work

“…Notice, in Fig. 3, that the scale combinator [19] is simply multiplication of a contract by a floating-point observable. In a domain specific language like BCL, it is convenient to reuse the ** multiplication syntax for scale as well.…”

“…It is first helpful to understand that BCL is predominantly used to model financial contracts, by providing end users with programmatic access to a financial contract library. The library we use is based upon the composable contracts of Peyton Jones, Eber and Seward [19]. Its internal contract data structure is used throughout our broader derivatives system to support various downstream analyses.…”

“…This is in contrast to "American" options, where the holder may choose to buy (or sell) on any date within a specified range of dates. This stock option is based on several helper functions, defined in [19], which we must examine first. The european function constructs a contract which allows its holder to choose between receiving "something" or nothing on a specified date.…”

A formalization of a startup finance transaction model using Alloy

“…Distinction between actual and diluted shares. 3. Difference in the price each investor paid for shares, and the respective investment cost must be recorded properly to calculate returns in case the company is acquired or goes public.…”

“…Although Simon P. Jones' paper provides a comprehensive formal semantics for the evaluation of derivative contracts, a similar formal semantics for capitalization tables remains absent from existing literature [3]. Financial instruments compose into a big expression that can evaluated to the raw dollars.…”