Date post: | 12-Apr-2017 |
Category: |
Economy & Finance |
Upload: | dragisa-zunic |
View: | 35 times |
Download: | 0 times |
Certified symbolic management of financialmultiparty contracts 1
Dragisa ZunicMeta-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
Examples :�� ��1 of 4
I we use examples from foreign exchange (FX) marketI days as a basic time unitI first we look at a forward contract
�� ��3 / 21
Examples :�� ��2 of 4
I because we want to represent American option..I the language has the conditional : if..within..then..else..I one party may, at any time before the contract ends, decide to
execute a purchase
�� ��4 / 21
Examples :�� ��3 of 4
I next we deal with an asian optionI on a set date in the future, a party may decide to buy an
underlying (or not to buy)I but the price is established from an of past prices (all the days)
�� ��5 / 21
Examples :�� ��4 of 4 (multiparty contract)
I to illustrate the multiparty aspect of the languageI consider credit default swap (CDS) on a zero-coupon bond
�� ��6 / 21
Examples :�� ��4 of 4 (multiparty contract)
I the above bond contract is denoted cbond , and CDS contractcCDS
I when we combine them as cbond&cCDS we get the contractwe wanted : CDS for a zero coupon bond
I compound contract - Y acts as both holder of the bond, andbuyer of the CDS
I Y interacts with both X and Z �� ��7 / 21
Examples :�� ��4 of 4 (multiparty contract)
I compound contract - Y acts as both holder of the bond, andbuyer of the CDS
I Y interacts with both X and Z
�� ��8 / 21
Syntax and type system
I An overview of the contract language - including theexpression sub-language
I l ∈ Label - refers to observables (eg., interest rate, X exercisesan option, etc.)
I p, q ∈ Party - refers to participants / partiesI a ∈ Asset - refers toI x ∈ Var - refers to expressions �� ��9 / 21
Syntax and type system
I we assume that each label in Label is assigned a unique typeτ , and we write Labelτ for the set of labels of type τ
I examples : “FX(USD,DKK)” ∈ LabelReal , and “X exercisesoption” ∈ LabelBool
I sometimes a party/client has control over an observable �� ��10 / 21
Syntax and type system
I The form let x = e in c - evaluates expression e at a currenttime, and stores the resulting value in x, for later reference inthe contract c
�� ��12 / 21
Syntax and type system
I For example, write an option contract that is cancelledas soon as a foreign exchange rate rises beyond the previouslyobserved exchange rate (threshold) :
�� ��13 / 21
Next
I Contract causality - only allow for contracts that make sense.Namely input from the external environment of tomorrowshould not influence cash-flow of today - Such contracts arenot causal.
I eg. cash-flow today specified by an exchange rate of tomorrow
I Contract horizon - definition
I Refined original typing rules - so that the well typedcontracts are causal
I Theorem : If contract is well typed then it is causal
I Theorem : Type inference is sound and complete
�� ��19 / 21
Content of research
I an expressive multi-party contract DSL
I a type system that statically ensures the that the contractsfollow the principle of causality
I a reduction semantics that for the contract language, whichevolves contracts over time, in accordance with thedenotational semantics
I formally verified correctness : type inference, reductionsemantics, contract specialisation and horizon inference
I using the code extraction of Coq, to generate Haskel code forcontract certified analysis and transformation
�� ��20 / 21
Sources
I Certified symbolic management of financial multi-partycontracts → http://dl.acm.org/citation.cfm?id=2784747
I Implementations in Coq and Haskell →https://github.com/HIPERFIT/contracts
I Composing contracts : an adventure in financial engineering→ http://dl.acm.org/citation.cfm?id=351267
Thank you
�� ��21 / 21