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L.G.H.C. Nalinda
2011CS005
11000058
Domain Specific Language for
Specify Operations of a Central
Counterparty
Supervisor: ...
Domain Specific Language to Define Operations for
Central Counterparty
▷Domain – Financial Market
▷Central Counterparty (C...
Road Map
▷Financial Contracts
▷Motivation
▷Research Hypothesis
▷Research Literature
▷Design
▷Representation Of CCP Operati...
Financial Contracts
Financial Contract
▷Financial Contract = Promise + Legal
▷Transfer $100 On 31st Dec. 2016
Future Date Promise
Future Cash ...
Motivation
DSL for Finance Sector
Motivation
Haskell Contract Combinator
Library
Peyton Jones, Marc-Eber, Julian (2000)
▷Fixed, Precisely Specified Set of Combinators (Unified Mechanism)
▷Describe a Cont...
Primitives for Defining Contracts | HCCL
IntroductionHCCL
Primitives for Defining Observables
IntroductionHCCL
Composing Contracts
Composing ZCB
“Receive £200 on Future Date t1”
C1 = one GBP
C2 = truncate t1 (one GBP)
= truncate t1 (C1)
C3 = scale 200 (...
Contract Definitions
IntroductionComposing Contracts
▷ZCB :: Date  Double  Currency  Contract
▷EU_OPTION :: Date  Cont...
Central Counterparty
Absence of CCP
CCP
With CCP
CCP
Operations of CCP
▷Margin Calculation
Purpose : No Counterparty Default Occur
At the End of Each Business Day
.
▷Possibili...
Rule 9102 – Long Option Position
Margin Requirement
.
Methodology
the period to expiry is greater or equal to 9
months, 50...
Research Hypothesis
If we can use Peyton Jones’s
language to compose FC/FD, we
can use the same language to
compose CCP Rules
Research Literature
Summary
IntroductionResearch Literature
DSL for Finance Sector Has been a Major Requirement Since Early Days
Payton, Eber,...
Design
Rule | Design Architecture IntroductionDesign
Seed Contract | Hypothesis
IntroductionDesign
Operations of CCP
IntroductionDesign
Representation of CCP
Operations
Sell 100 Dell shares for a
price of £4800 anywhere from
today to 240 days from today,
or DO NOTHING at all during the
time
Contract | Analysis
▷Giving user a “Choice”  Option Contract
Compose Option Contract using HCCL
▷Receive £ 4800 : C1 = (Get (Scale (Obs [4800.0]) (One GBP)))
▷Transfer(Sell) 100 Dell ...
Compose Option Contract using HCCL (Cntd.)
▷Composite Contract : C3 = And C1 C2
▷Adding Option to Contract : C4 = Or C3 Ze...
Instrument
▷Easy Way to Introduce
▷Grasp underlying rights and obligations  Name
Option Premium
▷Amount Pay For The Instrument
▷Option Premium Is A Contract
▷Pay £ 200 To Purchase “ABC_Instrument”
Trunca...
Trade Creation
Buyer Is
The
OWNER
Data Type| Trade
data Trade = Trade Instrument Contract
▷Trade
Option Premium Paid – £ 200
Instrument Purchased – “ABC_Ins...
Rights and Obligations Defined In Trade
▷Owner
-Sell 100 Dell + Receive 4800 GBP
or
- DO NOTHING
Trade Novation
▷Buyer | Owner – Long Position
▷Seller | Option Writer – Short Position
Analyze Trade
▷Get Instrument From Trade
▷Get Option Premium From Trade
Progress
Analyze Instrument
▷Equity (Equity) - Dell
▷Maturity Date (Int) - 240
▷Number Of Shares – (Obs Double) – (Obs 100.0)
▷Amou...
Long Option Position
Progress
Composing Rule 9102 | (a)
▷Options’ Time Value
- Time Varying Quantity
- Observable Double (Obs Double (eg. Obs 200))
- Co...
Composing Rule 9102 | (b)
▷Normal Margin (o1)
- Time Varying Quantity
- Observable Double (Obs Double)
▷In The Money Value...
Composing Rule 9102
Composing Rule 9102
▷rule9102One
▷rule9102Two
▷rule9102Composite
Research Hypothesis Proved
Evaluation & Analysis
Environment
▷Facts About Observables and Choices – Symbolic Management of Derivatives
- External to the FC/FD
- Direct imp...
Rule Equivalence(via Contract Equivalence)
▷Contract Equivalence
Same Environments
Two Different Contracts
Contracts Are I...
▷Rule Equivalence
Same Environments
Two Different Rules
Rules Are Identical In That Environment
GIVEN NOVATED CONTRACT
Eva...
Rules Transformation (via Contract Transformation)
▷Contract Transformation
Specialization Function “f”
Partial Evaluation...
▷Rules (Seed Contract) Transformation
Specialization Function “f”
Partial Evaluation Of Contract “Cseed”  f(Cseed,ρ)
New ...
Rule Decomposition(via Contract Decomposition)
▷Rule 9102
rule9102One
rule9102Two
Evaluation And Analysis
Data Types: Instrument
Evaluation And Analysis
Equality of Two Instruments
Evaluation And Analysis
New Instruments From Existing Instruments
Evaluation And Analysis
Data Types: Trade
Evaluation And Analysis
▷Purpose – Isolating Operations That Can Perform On Data Types
▷Decouple Each Le...
Margin Calculation Engine For CCP
Evaluation And Analysis
Conclusion and Future Work
Conclusion
Conclusion and Future Work
Conclusion
▷ Proved Hypothesis – Haskell Contract Combinator Library  CCP Rules
▷DSL approach “Margin Calculation”
lucrat...
Future Work
▷Put Option Only (Other Contract types)
▷Novation – Only one side analyzed
- Two Option Positions
- Long Optio...
THANK YOU 
Q&A
Rule Monotonicity (via Contract Monotonicity)
▷Contract Monotonicity
Two Different Environments
Partially Agree
Given Cont...
▷Rule Monotonicity
- Two Different Environments
- Partially Agree
- Given Rules Yield Same Cash Flow
- GIVEN NOVATED CONTR...
Financial Markets
Peyton Jones, Marc-Eber, Julian (2000)
▷Fixed, Precisely Specified Set of Combinators
▷Describe a Contract
▷Process a Cont...
Market Observables
Evaluation And Analysis
▷Addition
▷Division
▷Minimum
Gaillardet Observable Values Must Be:
- Boolean
- ...
Haskell Pattern Matching
IntroductionResearch Literature
Complex Derivatives
▷Mediratta – Credit Default Swap & Power Reverse Dual Currency Swap
▷Valuation – evalC :: Model  Cont...
Composing Rule 9102 | (a)
▷Date
▷Option’s Time Value in Double
▷Currency
Software Language Approach
▷Peyton – Justify that FP Approach Can Use to Define and Value Derivatives
- Lacking Highlighti...
Option Time Value
▷Time Value = Option Price – Intrinsic Value
▷Intrinsic Value – Price at which the Commodity is being tr...
After Novation
▷Buyer And Seller Treat Separately
▷Margin Calculation Is IMPORTANT
▷Constructing Core Level Contracts (
▷P...
Operations of CCP
▷Get Instrument From Trade
▷Get Option Premium From Trade
▷Analyze Instrument
Instrument Name
Equity
Mat...
Stakeholder Interests vs Economic Stability
▷History
Enron
2007 2008 Crisis
Greek Crisis
▷Minimize Risk– Effective Derivat...
Stock Exchanges (SE)
▷Buyers and Sellers Meet
▷Financial Contracts/ Financial Derivatives
Legal Contracts
Types: Futures, ...
Effective Derivative Mgt
▷Stakeholder Expectations vs Economic Stability
▷History
Enron
2007 2008 Crisis
Greek Crisis
▷Rul...
Effective Derivative Mgt(Cntd.)
▷Minimize Risk
▷Types of Risk
Operational, Legal
Business, Financial
▷Computer Science
Big...
ZCB(Contd.)
“Pay € 100 on Future Date t2”
C5 = give (scale 200 (truncate t2 (one EUR)))
IntroductionQ&A
Currency - €/EUR
D...
Composing European Option
C 7 = European (date “02 Sep 2015”)
( zcb (date “09 Nov 2016”) 0.4 GBP `and`
zcb (date “12 Oct 2...
Peyton Jones (Cntd)
▷Value Process – a Partial Function of Time
How Much this Contract Worth
Incorporate Environment Condi...
Peyton Jones (Cntd)
IntroductionResearch Literature
Peyton Jones (Cntd)
Model
IntroductionResearch Literature
Semantics for Contracts | VP IntroductionQ&A
Semantics for Observables | VP
IntroductionQ&A
Denotational Semantics | Gaillourdet
IntroductionQ&A
Software Language Approach (Cntd.)
▷Observable Value – Boolean | Real | Integer
▷Time – Natural Number
▷Constant K – Boole...
Software Language Approach (Cntd.)
▷Denotational Semantics – Map Each of Programs to Mathematical Object
- Denotation for ...
Symbolic Contract Management
▷Symbolic Contract Management – Why symbolic – Ease of Expressing
- Denotational Semantics In...
Symbolic Contract Management
▷Specialization–
▷Reduction
IntroductionResearch Literature
Architecture | Motivation IntroductionQ&A
Tree Representation IntroductionQ&A
C5
And
Or
Or
And C4
C3
C2C1
(Obs Double) to Double
▷Contracts (Double)
Amount Paid
# of Shares Traded ++
▷Extracted Values + Computations (Obs Double)...
(Obs Double) to Double (Cntd.)
▷Double  (Obs Double)
konst
▷(Obs Double)  (Double)
Our Own Function
Methodology
(Obs Double) to Double (Cntd.)
Methodology
A : Show a => a -> String (String representation of the value)
B : matchRegex (...
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Domain Specific Language for Specify Operations of a Central Counterparty(CCP)

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Financil Contracts (FCs) specify rights and obligations that parties are legally
bind.Hence effective management of FCs is vital.Domain Specific Language (DSL)
approach provides a method of defining rights and obligations of contracts using fixed
and precisely defined set of combinators and observables.As a result, any contract can
be composed using fixed set of symbols, the contract management becomes efficient and effective.The Haskell Contract Combinator Library (HCCL) is the driving forcebehind the DSL approach in finance sector

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Domain Specific Language for Specify Operations of a Central Counterparty(CCP)

  1. 1. L.G.H.C. Nalinda 2011CS005 11000058 Domain Specific Language for Specify Operations of a Central Counterparty Supervisor: Dr. Chamath Keppetiyagama
  2. 2. Domain Specific Language to Define Operations for Central Counterparty ▷Domain – Financial Market ▷Central Counterparty (CCP) – Financial Institute Financial Market Specific Language to CCP
  3. 3. Road Map ▷Financial Contracts ▷Motivation ▷Research Hypothesis ▷Research Literature ▷Design ▷Representation Of CCP Operations ▷Evaluation & Analysis ▷Conclusion And Future Work
  4. 4. Financial Contracts
  5. 5. Financial Contract ▷Financial Contract = Promise + Legal ▷Transfer $100 On 31st Dec. 2016 Future Date Promise Future Cash Flow ▷Different Contracts  Different Purposes Different Interests Contract Definitions Different Different Operations
  6. 6. Motivation
  7. 7. DSL for Finance Sector Motivation
  8. 8. Haskell Contract Combinator Library
  9. 9. Peyton Jones, Marc-Eber, Julian (2000) ▷Fixed, Precisely Specified Set of Combinators (Unified Mechanism) ▷Describe a Contract ▷Process a Contract ▷Find Value of a Contract ▷Compositional Nature – (Can Glue Combinators Together) Contract Primitives + Observable Primitives IntroductionHCCL
  10. 10. Primitives for Defining Contracts | HCCL IntroductionHCCL
  11. 11. Primitives for Defining Observables IntroductionHCCL
  12. 12. Composing Contracts
  13. 13. Composing ZCB “Receive £200 on Future Date t1” C1 = one GBP C2 = truncate t1 (one GBP) = truncate t1 (C1) C3 = scale 200 (truncate t1(one GBP)) = scale 200 (C2) C4 = get (scale 200 (truncate t1(one GBP))) get (C3) IntroductionComposing Contracts ZCB :: Date -> Double -> Currency -> Contract
  14. 14. Contract Definitions IntroductionComposing Contracts ▷ZCB :: Date  Double  Currency  Contract ▷EU_OPTION :: Date  Contract  Contract ▷AMERICAN_OPTION :: (Date,Date)  Contract  Contract
  15. 15. Central Counterparty
  16. 16. Absence of CCP CCP
  17. 17. With CCP CCP
  18. 18. Operations of CCP ▷Margin Calculation Purpose : No Counterparty Default Occur At the End of Each Business Day . ▷Possibilities Dr. Trader Account Cr. Trader Account Restate to Initial Margin CCP
  19. 19. Rule 9102 – Long Option Position Margin Requirement . Methodology the period to expiry is greater or equal to 9 months, 50% of the option’s time value, else 100% of the option’s time value Future Cash Flow .
  20. 20. Research Hypothesis
  21. 21. If we can use Peyton Jones’s language to compose FC/FD, we can use the same language to compose CCP Rules
  22. 22. Research Literature
  23. 23. Summary IntroductionResearch Literature DSL for Finance Sector Has been a Major Requirement Since Early Days Payton, Eber, Julian HCCL Mediratta Complex Derivatives Gaillourdet Software Language Approach Bahr, Jost, Elsman Symbolic Management of Finance Contracts & Symbolic Management of Multiparty Contracts CCP Operations Have Not Yet Addressed using DSL Approach
  24. 24. Design
  25. 25. Rule | Design Architecture IntroductionDesign
  26. 26. Seed Contract | Hypothesis IntroductionDesign
  27. 27. Operations of CCP IntroductionDesign
  28. 28. Representation of CCP Operations
  29. 29. Sell 100 Dell shares for a price of £4800 anywhere from today to 240 days from today, or DO NOTHING at all during the time
  30. 30. Contract | Analysis ▷Giving user a “Choice”  Option Contract
  31. 31. Compose Option Contract using HCCL ▷Receive £ 4800 : C1 = (Get (Scale (Obs [4800.0]) (One GBP))) ▷Transfer(Sell) 100 Dell Shares : C2 : (Give (Scale(Obs [100.0]) (OneE DEL))
  32. 32. Compose Option Contract using HCCL (Cntd.) ▷Composite Contract : C3 = And C1 C2 ▷Adding Option to Contract : C4 = Or C3 Zero ▷Maturity @240th day: C5 = Truncate 240 C4
  33. 33. Instrument ▷Easy Way to Introduce ▷Grasp underlying rights and obligations  Name
  34. 34. Option Premium ▷Amount Pay For The Instrument ▷Option Premium Is A Contract ▷Pay £ 200 To Purchase “ABC_Instrument” TruncateT ((),1) (Scale (Obs [200.0]) (One GBP))
  35. 35. Trade Creation Buyer Is The OWNER
  36. 36. Data Type| Trade data Trade = Trade Instrument Contract ▷Trade Option Premium Paid – £ 200 Instrument Purchased – “ABC_Instrument” Underlying Contract – Option Created This Trade Brings To CCP
  37. 37. Rights and Obligations Defined In Trade ▷Owner -Sell 100 Dell + Receive 4800 GBP or - DO NOTHING
  38. 38. Trade Novation ▷Buyer | Owner – Long Position ▷Seller | Option Writer – Short Position
  39. 39. Analyze Trade ▷Get Instrument From Trade ▷Get Option Premium From Trade Progress
  40. 40. Analyze Instrument ▷Equity (Equity) - Dell ▷Maturity Date (Int) - 240 ▷Number Of Shares – (Obs Double) – (Obs 100.0) ▷Amount To Be Paid – (Obs Double) – (Obs 4800) ▷Currency – (Currency) – GBP (£) ▷Amount Paid (Obs Double) – (Obs 200) ▷Currency – (Currency) – GBP (£) Progress Analyze Option Premium
  41. 41. Long Option Position Progress
  42. 42. Composing Rule 9102 | (a) ▷Options’ Time Value - Time Varying Quantity - Observable Double (Obs Double (eg. Obs 200)) - Compute following, Option Premium Paid (Obs Double) - lift2 Operator Of HCCL - Convert (Obs Double) to Double using Haskell inbuilt functions
  43. 43. Composing Rule 9102 | (b) ▷Normal Margin (o1) - Time Varying Quantity - Observable Double (Obs Double) ▷In The Money Value (o2) - Time Varying Quantity - Observable Double (Obs Double) ▷Lesser - Observable Comparison lift2 min o1 o2
  44. 44. Composing Rule 9102
  45. 45. Composing Rule 9102 ▷rule9102One ▷rule9102Two ▷rule9102Composite
  46. 46. Research Hypothesis Proved
  47. 47. Evaluation & Analysis
  48. 48. Environment ▷Facts About Observables and Choices – Symbolic Management of Derivatives - External to the FC/FD - Direct impact on the FC/FD IntroductionResearch Literature
  49. 49. Rule Equivalence(via Contract Equivalence) ▷Contract Equivalence Same Environments Two Different Contracts Contracts Are Identical In That Environment Evaluation And Analysis Patrick Bhar
  50. 50. ▷Rule Equivalence Same Environments Two Different Rules Rules Are Identical In That Environment GIVEN NOVATED CONTRACT Evaluation And Analysis
  51. 51. Rules Transformation (via Contract Transformation) ▷Contract Transformation Specialization Function “f” Partial Evaluation Of Contract “C”  f(C,ρ) New Environment - ρʹ Same Cash Flows Evaluation And Analysis Patrick Bhar
  52. 52. ▷Rules (Seed Contract) Transformation Specialization Function “f” Partial Evaluation Of Contract “Cseed”  f(Cseed,ρ) New Environment - ρʹ Same Cash Flows Evaluation And Analysis
  53. 53. Rule Decomposition(via Contract Decomposition) ▷Rule 9102 rule9102One rule9102Two Evaluation And Analysis
  54. 54. Data Types: Instrument Evaluation And Analysis
  55. 55. Equality of Two Instruments Evaluation And Analysis
  56. 56. New Instruments From Existing Instruments Evaluation And Analysis
  57. 57. Data Types: Trade Evaluation And Analysis ▷Purpose – Isolating Operations That Can Perform On Data Types ▷Decouple Each Level Of Contract Management Via New Data Types ▷Only Core Operations
  58. 58. Margin Calculation Engine For CCP Evaluation And Analysis
  59. 59. Conclusion and Future Work
  60. 60. Conclusion Conclusion and Future Work
  61. 61. Conclusion ▷ Proved Hypothesis – Haskell Contract Combinator Library  CCP Rules ▷DSL approach “Margin Calculation” lucrative Easy (fixed set of combinators and observables) ▷Symbolic Management Rule Equivalence Rule Transformation Rule Decomposition (Rule Monotonicity) ▷Base research for CCP Conclusion And Future Work
  62. 62. Future Work ▷Put Option Only (Other Contract types) ▷Novation – Only one side analyzed - Two Option Positions - Long Option Position  - Short Option Position ??? - Netting and Position Calculation (new observables ?) ▷One Rule – Rule 9102 ▷Type Conversion ▷Margin Calculation Engine IntroductionConclusion And Future Work Mediratta CS+Finance+Maths UI Skilled People
  63. 63. THANK YOU 
  64. 64. Q&A
  65. 65. Rule Monotonicity (via Contract Monotonicity) ▷Contract Monotonicity Two Different Environments Partially Agree Given Contract Yield Same Cash Flow Evaluation And Analysis Patrick Bhar
  66. 66. ▷Rule Monotonicity - Two Different Environments - Partially Agree - Given Rules Yield Same Cash Flow - GIVEN NOVATED CONTRACT Evaluation And Analysis
  67. 67. Financial Markets
  68. 68. Peyton Jones, Marc-Eber, Julian (2000) ▷Fixed, Precisely Specified Set of Combinators ▷Describe a Contract ▷Process a Contract ▷Find Value of a Contract ▷Compositional Nature Contract Primitives + Observable Primitives IntroductionResearch Literature
  69. 69. Market Observables Evaluation And Analysis ▷Addition ▷Division ▷Minimum Gaillardet Observable Values Must Be: - Boolean - Real Number - Integer ▷Options Time Value ▷In The Money Value ▷Margin Required ▷Intrinsic Value
  70. 70. Haskell Pattern Matching IntroductionResearch Literature
  71. 71. Complex Derivatives ▷Mediratta – Credit Default Swap & Power Reverse Dual Currency Swap ▷Valuation – evalC :: Model  Contract - evalO :: Model  Contract More Complex Derivatives Can Compose Using Fixed Set of Combinators & Observables While Preserving Uniqueness of the Contract IntroductionResearch Literature
  72. 72. Composing Rule 9102 | (a) ▷Date ▷Option’s Time Value in Double ▷Currency
  73. 73. Software Language Approach ▷Peyton – Justify that FP Approach Can Use to Define and Value Derivatives - Lacking Highlighting SE Language Concepts - No Unified Approach  ▷Gaillourdet – HCCL in a SW Language Point of View - Provided a Formal Definition for the Language (Syntax) Syntax of Observables Syntax of Contract - Denotational Semantics Observables Contracts IntroductionResearch Literature
  74. 74. Option Time Value ▷Time Value = Option Price – Intrinsic Value ▷Intrinsic Value – Price at which the Commodity is being traded at considered date. Observable  Obs Double ▷In the Money -> Strike Price Vs Spot Rate IntroductionResearch Literature
  75. 75. After Novation ▷Buyer And Seller Treat Separately ▷Margin Calculation Is IMPORTANT ▷Constructing Core Level Contracts ( ▷Partial Contract Implementation ▷Construction of Rule Using HCCL ▷Finalizing Seed Contract ▷Generate All Possible Results Progress Work In Progress
  76. 76. Operations of CCP ▷Get Instrument From Trade ▷Get Option Premium From Trade ▷Analyze Instrument Instrument Name Equity Maturity Number Of Shares Traded Amount Agree To Pay Currency ▷Analyze Option Premium
  77. 77. Stakeholder Interests vs Economic Stability ▷History Enron 2007 2008 Crisis Greek Crisis ▷Minimize Risk– Effective Derivative Management ▷Computer Science Big Data Data Mining Real Time Analytics Neural Networks ++ Financial Markets
  78. 78. Stock Exchanges (SE) ▷Buyers and Sellers Meet ▷Financial Contracts/ Financial Derivatives Legal Contracts Types: Futures, Options, Swaps, Swaptions, Bonds ++ CDS, PRDC Swaps ++ ▷Rules and Regulations Uncertainty Effective Derivative & Contract mgt: Financial Markets
  79. 79. Effective Derivative Mgt ▷Stakeholder Expectations vs Economic Stability ▷History Enron 2007 2008 Crisis Greek Crisis ▷Rules and Regulations Uncertainty Effective Derivative & Contract mgt: Financial Markets
  80. 80. Effective Derivative Mgt(Cntd.) ▷Minimize Risk ▷Types of Risk Operational, Legal Business, Financial ▷Computer Science Big Data Data Mining Real Time Analytics Neural Networks ++ Financial Markets
  81. 81. ZCB(Contd.) “Pay € 100 on Future Date t2” C5 = give (scale 200 (truncate t2 (one EUR))) IntroductionQ&A Currency - €/EUR Date - t2 Action - “Pay” Amount - £200 and :: Contract -> Contract -> Contract C4 = get (scale 200 (truncate t2 (one GBP))) C5 = give (scale 100 (truncate t2 (one EUR))) C6 = and C4 C5
  82. 82. Composing European Option C 7 = European (date “02 Sep 2015”) ( zcb (date “09 Nov 2016”) 0.4 GBP `and` zcb (date “12 Oct 2016”) 8.4 USD `and` zcb (date “18 Nov 2016”) 0.4 GBP `and` give (zcb (date “09 Nov 2016”) 0.4 GBP) C8 = European Option = C7 `or` zero IntroductionQ&A European :: Date -> Contract -> Contract
  83. 83. Peyton Jones (Cntd) ▷Value Process – a Partial Function of Time How Much this Contract Worth Incorporate Environment Conditions Generating Information from Defined Contract ▷Abstract Evaluation – How to Translate Arbitrary Contract into a Value Process - Semantics for Contract Primitives - Semantics for Observables ▷Concrete Implementation – Implementation of Abstract Semantics - Model IntroductionResearch Literature
  84. 84. Peyton Jones (Cntd) IntroductionResearch Literature
  85. 85. Peyton Jones (Cntd) Model IntroductionResearch Literature
  86. 86. Semantics for Contracts | VP IntroductionQ&A
  87. 87. Semantics for Observables | VP IntroductionQ&A
  88. 88. Denotational Semantics | Gaillourdet IntroductionQ&A
  89. 89. Software Language Approach (Cntd.) ▷Observable Value – Boolean | Real | Integer ▷Time – Natural Number ▷Constant K – Boolean | Real | Integer ▷Unknown Observables – “S” ▷Binary Operators & Comparison Operators – Two Arguments of Same Type - Binary – Returns Same Type - Comparison – Returns Boolean ▷Unary – One Argument and Return Same Type ▷Type Casting – (C2D o | D2C o) IntroductionResearch Literature
  90. 90. Software Language Approach (Cntd.) ▷Denotational Semantics – Map Each of Programs to Mathematical Object - Denotation for Observables - Denotation for Contracts ▷Denotation for Observables – (S  N  V)  ( N  V ) ▷Denotation for Contracts – (S  N  V)  ( N  D ) ▷“e” – Environment IntroductionResearch Literature
  91. 91. Symbolic Contract Management ▷Symbolic Contract Management – Why symbolic – Ease of Expressing - Denotational Semantics Information - Expression (Set of Symbols) - Monotonicity (Europe vs Asia) ▷Contract Management and Analysis - Contract Equivalence - Inferring Contract Properties - Contract Dependence (Observables Affect on Cash Flows) - Contract Causality (Future Observable) - Contract Horizon (Life Time) ▷Contract Transformation – Specialization & Reduction IntroductionResearch Literature
  92. 92. Symbolic Contract Management ▷Specialization– ▷Reduction IntroductionResearch Literature
  93. 93. Architecture | Motivation IntroductionQ&A
  94. 94. Tree Representation IntroductionQ&A C5 And Or Or And C4 C3 C2C1
  95. 95. (Obs Double) to Double ▷Contracts (Double) Amount Paid # of Shares Traded ++ ▷Extracted Values + Computations (Obs Double) Time Value Intrinsic Value ++ eg: The Lesser of Normal Margin And In The Money Value Methodology
  96. 96. (Obs Double) to Double (Cntd.) ▷Double  (Obs Double) konst ▷(Obs Double)  (Double) Our Own Function Methodology
  97. 97. (Obs Double) to Double (Cntd.) Methodology A : Show a => a -> String (String representation of the value) B : matchRegex (Regex  String  Maybe[String]) "[-+]?([0-9]*.[0-9]+|[0-9]+)“ C : fromJust :: Maybe a -> a D : Operator (!!) E : read a :: Double

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