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Financial-multiparty-contracts bahr-berthold-elsman dragisa-zunic

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Partial review of work presented in the article: http://dl.acm.org/citation.cfm?id=2784747

Domain specific language for financial derivatives, including multiparty aspect. Certified implementation using Coq proof assistant - and extraction of Haskell code.

Published in: Economy & Finance
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Financial-multiparty-contracts bahr-berthold-elsman dragisa-zunic

  1. 1. Certified symbolic management of financial multiparty contracts 1 Dragiˇsa ˇZuni´c Meta-CLF2 reading group February 20, 2017. 1. Research by P. Bahr, J. Berthold and M. Elsman in http://dl.acm. org/citation.cfm?id=2784747 £   1 / 21
  2. 2. Examples : £ ¢   ¡1 of 4 we use examples from foreign exchange (FX) market days as a basic time unit first we look at a forward contract £   3 / 21
  3. 3. Examples : £ ¢   ¡2 of 4 because we want to represent American option.. the language has the conditional : if..within..then..else.. one party may, at any time before the contract ends, decide to execute a purchase £   4 / 21
  4. 4. Examples : £ ¢   ¡3 of 4 next we deal with an asian option on a set date in the future, a party may decide to buy an underlying (or not to buy) but the price is established from an of past prices (all the days) £   5 / 21
  5. 5. Examples : £ ¢   ¡4 of 4 (multiparty contract) to illustrate the multiparty aspect of the language consider credit default swap (CDS) on a zero-coupon bond £   6 / 21
  6. 6. Examples : £ ¢   ¡4 of 4 (multiparty contract) the above bond contract is denoted cbond , and CDS contract cCDS when we combine them as cbond &cCDS we get the contract we wanted : CDS for a zero coupon bond compound contract - Y acts as both holder of the bond, and buyer of the CDS Y interacts with both X and Z £   7 / 21
  7. 7. Examples : £ ¢   ¡4 of 4 (multiparty contract) compound contract - Y acts as both holder of the bond, and buyer of the CDS Y interacts with both X and Z £   8 / 21
  8. 8. Syntax and type system An overview of the contract language - including the expression sub-language l ∈ Label - refers to observables (eg., interest rate, X exercises an option, etc.) p, q ∈ Party - refers to participants / parties a ∈ Asset - refers to x ∈ Var - refers to expressions £   9 / 21
  9. 9. Syntax and type system we assume that each label in Label is assigned a unique type τ, and we write Labelτ for the set of labels of type τ examples : “FX(USD,DKK)” ∈ LabelReal , and “X exercises option” ∈ LabelBool sometimes a party/client has control over an observable £   10 / 21
  10. 10. Syntax and type system £   11 / 21
  11. 11. Syntax and type system The form let x = e in c - evaluates expression e at a current time, and stores the resulting value in x, for later reference in the contract c £   12 / 21
  12. 12. Syntax and type system For example, write an option contract that is cancelled as soon as a foreign exchange rate rises beyond the previously observed exchange rate (threshold) : £   13 / 21
  13. 13. Typing of expression operators £   14 / 21
  14. 14. Denotational semantics of expressions £   15 / 21
  15. 15. Denotational semantics of contracts : part 1 £   16 / 21
  16. 16. Denotational semantics of contracts : part 2 £   17 / 21
  17. 17. Equivalences on contracts £   18 / 21
  18. 18. Next Contract causality - only allow for contracts that make sense. Namely input from the external environment of tomorrow should not influence cash-flow of today - Such contracts are not causal. eg. cash-flow today specified by an exchange rate of tomorrow Contract horizon - definition Refined original typing rules - so that the well typed contracts are causal Theorem : If contract is well typed then it is causal Theorem : Type inference is sound and complete £   19 / 21
  19. 19. Content of research an expressive multi-party contract DSL a type system that statically ensures the that the contracts follow the principle of causality a reduction semantics that for the contract language, which evolves contracts over time, in accordance with the denotational semantics formally verified correctness : type inference, reduction semantics, contract specialisation and horizon inference using the code extraction of Coq, to generate Haskel code for contract certified analysis and transformation £   20 / 21
  20. 20. Sources Certified symbolic management of financial multi-party contracts → http://dl.acm.org/citation.cfm?id=2784747 Implementations in Coq and Haskell → https://github.com/HIPERFIT/contracts Composing contracts : an adventure in financial engineering → http://dl.acm.org/citation.cfm?id=351267 Thank you £   21 / 21

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