Formal reasoning about financial derivatives- introduction -

Dragisa Zunic

Project Meta-CLF2 - reading group

Carnegie Mellon University QatarIT University of Copenhagen

February 13, 2017. �� ��1 / 29

General context including (known) commercial aspects

I in the year 2000 : Peyton Jones, Eber and Seward, publishedan article “Composing contracts : an adventure in financialengineering” (at ICFP)

I related research, eg. in 2009 : “Commercial uses : goingfunctional on exotic trades”, by Frankau, Spinellis et al. (inJFP)

I recent research from 2015 : “Certified symbolic managementof financial multi-party contracts”, by Bahr, Berthold andElsman” (at ICFP)

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General context including (known) commercial aspects

I LexiFi, by Jean Marc Eber (Paris, since 2000.) ; relies onPeyton Jones, Seward and Eber’s research

Provides a software for pricing and management of derivativesand structured products

“Instrument box”, as a core product, can be embedded into3rd party applications ; LexiFi’s “instrument box” used byBloomberg platform, since 2016.

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General context including commercial aspects

I Aesthetic Integration (London, since 2015), by G. Passmoreand D. Ignatovich ; won a finance technology competitionamong 600 projects worldwide

Given a model and a property to reason about, Imandra worksto generate a proof that the property will always hold, or topresent a concrete counterexample identifying how theproperty may be violated.

Fomal verification on ethereum. “Imandra” as a core product

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I paper presented at the International Conference on FunctionalProgramming, ICFP, 2000 in Montreal

I won the best-paper award, I think

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Composing contracts : an adventure in financialengineering

I introduce a combinator library

I that allows to describe financial contracts

I and a compositional denotational semantics

I that says what such contracts are worth

I Using Haskell for implementation

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Composing contracts : an adventure in financialengineering

I introduce a combinator library

I that allows to describe financial contracts

I and a compositional denotational semantics

I that says what such contracts are worth

I Using Haskell for implementation

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Composing contracts : an adventure in financialengineering

I introduce a combinator library

I that allows to describe financial contracts

I and a compositional denotational semantics

I that says what such contracts are worth

I Using Haskell for implementation

�� ��6 / 29

Composing contracts : an adventure in financialengineering

I introduce a combinator library

I that allows to describe financial contracts

I and a compositional denotational semantics

I that says what such contracts are worth

I Using Haskell for implementation

�� ��6 / 29

Composing contracts : an adventure in financialengineering

I introduce a combinator library

I that allows to describe financial contracts

I and a compositional denotational semantics

I that says what such contracts are worth

I Using Haskell for implementation

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I companies have these in a catalogue - as prefabricated components

I often people need a contract that is not in the catalogue

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Question : can all these be defined using a set of preciselyspecified set of primitives or combinators ?

If yes, then we

I can describe new, unforseen, contracts

I can systematically analyze and perform computation over the newcontracts

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Getting started - a contract illustration

Zero-coupon bond (zcb) : “ Receive GBP 100 on 1st January2010”

We can specify this contract as :

c1 :: Contract

c1 = zcb t1 100 GBP

Where zcb is of type:

zcb :: Date -> Double -> Currency -> Contract �� ��9 / 29

Getting started

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Getting started - combining contracts : and

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Getting started - combining contracts : give

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Getting started - combining contracts : a newcombinator

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Primitives for defining�� ��contracts

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Primitives for defining�� ��contracts

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Primitives for defining�� ��contracts

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Primitives for defining�� ��contracts

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Primitives for defining�� ��contracts

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Primitives for defining�� ��contracts

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Primitives over�� ��observables

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Primitives over�� ��observables

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Primitives over�� ��observables

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Compositional evaluation semantics for�� ��contracts

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Evaluation semantics for�� ��observables

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Model primitives 1 of 2

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Model primitives 2 of 2

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Definition of horizon

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Sources

I Composing contracts : an adventure in financial engineering→ http://dl.acm.org/citation.cfm?id=351267

I Certified symbolic management of financial multi-partycontracts → http://dl.acm.org/citation.cfm?id=2784747

Thanks!

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