mandra Formal Verification of Financial Algorithms, Progress and Prospects Grant Olney Passmore ACL2-2017, Austin

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Austin Joint work with Denis Ignatovich and our

1 mandra Grant Olney Passmore Formal Verification of Financial Algorithms, Progress and Prospects ACL2-2017, Austin Joint work with Denis Ignatovich and our incredible team at AI DESIGNED WITH CARE BY AESTHE TIC INTEGRATI ON

2 Video (see it on The Logic of Financial Risk / 2

3 Problem Financial markets have become notoriously unstable. The Logic of Financial Risk / 3

4 Problem Financial markets have become notoriously unstable. Flash Crashes: systemic events characterised by non-trivial codependence of trading algorithms (e.g., May 2010, drop of $1tr) The Logic of Financial Risk / 4

5 Problem Financial markets have become notoriously unstable. Flash Crashes: systemic events characterised by non-trivial codependence of trading algorithms (e.g., May 2010, drop of $1tr) Lack of Transparency: issues of misrepresentation (e.g., misleading marketing materials or regulatory filings) of trading algorithm behaviour (e.g., BATS/Direct Edge $14M settlement with the SEC) The Logic of Financial Risk / 5

6 Problem Financial markets have become notoriously unstable. Flash Crashes: systemic events characterised by non-trivial codependence of trading algorithms (e.g., May 2010, drop of $1tr) Lack of Transparency: issues of misrepresentation (e.g. misleading marketing materials or regulatory filings) of trading algorithm behaviour (e.g., BATS/Direct Edge $14M settlement with the SEC) Glitches: trading system errors in design or implementation, often causing significant losses (e.g., Knight Capital s loss of $400M) The Logic of Financial Risk / 6

7 Goals for this talk Concepts: venue, exchange, dark pool, order book, order type (market, limit, pegged), matching logic, market microstructure, smart order router 7

8 Goals for this talk Concepts: venue, exchange, dark pool, order book, order type (market, limit, pegged), matching logic, market microstructure, smart order router Regulations: Transparency, safety and fairness (Reg ATS-N), best execution (Reg NMS)

9 Goals for this talk Concepts: venue, exchange, dark pool, order book, order type (market, limit, pegged), matching logic, market microstructure, smart order router Regulations: Transparency, safety and fairness (Reg ATS-N), best execution (Reg NMS) Practice: Be able to write a spec and analyse basic regulatory properties of a trading venue s matching logic

10 Goals for this talk Intuitions: Venue matching logics = ISA of the market Pressing need for: venues to be bullet-proof w.r.t. safety and fairness regulations matching logics to be formally described to regulators and market participants matching logics to be formally analysed w.r.t. precise encodings of regulatory directives financial mathematics (stochastic calculus) that takes precise discrete behaviour of matching logics into account

11 The Stack of Financial Algorithms The Logic of Financial Risk / 11

12 The Stack of Financial Algorithms Venues The Logic of Financial Risk / 12

13 The Stack of Financial Algorithms Smart Order Routers Venues The Logic of Financial Risk / 13

14 The Stack of Financial Algorithms Trading Algos Smart Order Routers Venues The Logic of Financial Risk / 14

15 The Stack of Financial Algorithms Algo Containers Trading Algos Smart Order Routers Venues The Logic of Financial Risk / 15

16 The Stack of Financial Algorithms Inventory Management Algo Containers Trading Algos Smart Order Routers Venues The Logic of Financial Risk / 16

17 The Stack of Financial Algorithms Collateral Trading Inventory Management Algo Containers Trading Algos Smart Order Routers Venues The Logic of Financial Risk / 17

18 The Stack of Financial Algorithms Collateral Trading Inventory Management Algo Containers Trading Algos Smart Order Routers Venues The Logic of Financial Risk / 18

19 The Stack of Financial Algorithms low freq Collateral Trading Inventory Management Algo Containers Trading Algos Smart Order Routers high freq Venues The Logic of Financial Risk / 19

20 The Stack of Financial Algorithms low freq Collateral Trading Inventory Management Algo Containers Trading Algos high freq Smart Order Routers Venues discrete, nonlinear The Logic of Financial Risk / 20

21 The Stack of Financial Algorithms low freq Collateral Trading Inventory Management Algo Containers Trading Algos continuous, nonlinear high freq Smart Order Routers Venues discrete, nonlinear The Logic of Financial Risk / 21

22 What is a venue? The Logic of Financial Risk / 22

23 What is a venue? The Logic of Financial Risk / 23

24 What is a venue? The Logic of Financial Risk / 24

25 What is a venue? LIT LIQUIDITY DARK LIQUIDITY The Logic of Financial Risk / 25

26 Running Example: UBS ATS First place winner! 620 companies 52 countries The Logic of Financial Risk TM

27 Running Example: UBS ATS First place winner! 620 companies 52 countries Jan, 2015: UBS fined $14M by the SEC for issues of unfairness in their dark pool design We analysed it, found more issues The Logic of Financial Risk TM

28 Running Example: UBS ATS The Logic of Financial Risk TM

29 Running Example: UBS ATS Let s examine an actual regulatory disclosure (esp. Sec 4.1) The Logic of Financial Risk TM

30 What is Imandra? Programming language Mathematical logic Reasoning engine The Logic of Financial Risk T M

31 What is Imandra? + Programming language Mathematical logic Reasoning engine Automated Reasoning First-class counterexamples Nonlinear + SE decomposition Proof automation for various financial regulations Test suite generation Documentation generation The Logic of Financial Risk T M

32 What does a venue do? maintain an order book process incoming orders match orders ( trade!) send `fills route orders away (`best-ex ) report on market activity all according to a (precisely?) defined spec while obeying many complex regulations The Logic of Financial Risk / 32

33 What is an order book? The Logic of Financial Risk / 33

34 What is an order book? The Logic of Financial Risk / 34

35 What is an order book? at each discrete time-step, the book is sorted. The Logic of Financial Risk / 35

36 What is an order book? how is it sorted? The Logic of Financial Risk / 36

37 What is an order book? how is it sorted? VERY COMPLEX ANSWER! The Logic of Financial Risk / 37

38 What is an order book? how is it sorted? INTUITION: Price/Time Priority The Logic of Financial Risk / 38

39 What is an order book? how is it sorted? INTUITION: Price/Time Priority REALITY: Let s see! The Logic of Financial Risk / 39

40 What is an order? an instruction to buy or sell a given security in a specified manner, subject to market constraints, and order parameters. The Logic of Financial Risk / 40

41 What is an order? an instruction to buy or sell a given security in a specified manner, subject to market constraints, and order parameters. buy 100 shares of MSFT, with price at most $50 The Logic of Financial Risk / 41

42 What is an order? an instruction to buy or sell a given security in a specified manner, subject to market constraints, and order parameters. buy 100 shares of MSFT, with price at most $50 buy 100 shares of MSFT The Logic of Financial Risk / 42

43 What is an order? The Logic of Financial Risk / 43

44 What is an order type? MARKET ORDER The Logic of Financial Risk / 44

45 What is an order type? MARKET ORDER LIMIT ORDER The Logic of Financial Risk / 45

46 What is an order type? MARKET ORDER LIMIT ORDER ICEBERG ORDER The Logic of Financial Risk / 46

47 What is an order type? MARKET ORDER LIMIT ORDER ICEBERG ORDER STOP LOSS ORDER The Logic of Financial Risk / 47

48 What is an order type? The Logic of Financial Risk / 48

49 What is an order type? The Logic of Financial Risk / 49

50 What is an order type? The Logic of Financial Risk / 50

Is your venue fair? Difficult questions: - Is your venue fair? - Can you prove it? - If it s not fair, how can you fix it? - Can your collection of order-types ever violate regulatory directives?

51 Is your venue fair? Difficult questions: - Is your venue fair? - Can you prove it? - If it s not fair, how can you fix it? - Can your collection of order-types ever violate regulatory directives? - Does your high-performance implementation conform to your highlevel design specification? - Does your documentation of your ordertypes truly match your implementation? - How can you automate both testing and compliance? - What is the strongest possible evidence you can give to regulators? The Logic of Financial Risk / 51

Formal analysis of trading venues Analysis of

way to manage growing order-type proliferation

52 Formal analysis of trading venues Analysis of safety and fairness properties of trading venues (dark pools, exchanges, etc.) In use at top global investment banks Principled way to manage growing order-type proliferation Exciting developments in regulatory space (more soon!) The Logic of Financial Risk / 52

53 Running Example: UBS ATS Demo: Transitivity of order ranking The Logic of Financial Risk / 53

54 Example: SIX Swiss Exchange The Logic of Financial Risk / 54

55 Pricing Logic: Informal The Logic of Financial Risk / 55

56 Pricing Logic: Formal The Logic of Financial Risk / 56

57 Pricing Fairness Example Consider specification of the SIX Swiss matching logic - we will prove that client ID, although used by the system, does not factor into pricing and matching decisions We will use IML to encode both the matching logic and the fairness principle, and then use Imandra to reason about the model Our example highlights iterative nature of the specification process: We discover, through a non-trivial counterexample, that our original hypothesis is incorrect. We then update our specification or model accordingly and iterate. The Logic of Financial Risk / 57

58 Pricing Fairness Example The following is an overview of the SIX Swiss Matching Engine Three market models: CLOB, MMB, and MMB-FoK Six business periods, 5 order types with numerous attributes 22 product types across equities, bonds, funds, and structured products with specific trading parameters Randomised auction times, volatility circuit breakers, order validities, and regulatory reporting requirements Complexity stems from the need to meet diverse client needs while operating a heavily regulated business The Logic of Financial Risk / 58

59 Pricing Fairness Example B_1 == B_2 except Client ID S_1 == S_2 except Client ID? MatchPrice(S) = MatchPrice(S ) The Logic of Financial Risk / 59

60 Pricing Fairness Example B_1 == B_2 except Client ID S_1 == S_2 except Client ID NO MatchPrice(S) = MatchPrice(S ) The Logic of Financial Risk / 60

61 Pricing Fairness Example B_1 == B_2 except Client ID S_1 == S_2 except Client ID YES MatchPrice(S) = MatchPrice(S ) The Logic of Financial Risk / 61

62 Principal Region Decomposition symbolic execution modulo nonlinear sign-invariance intuitively, a generalisation of cylindrical algebraic decomposition to programs the basis of IMANDRA s test-suite and documentation generation The Logic of Financial Risk /62

63 The Stack of Financial Algorithms low freq Collateral Trading Inventory Management Algo Containers Trading Algos Smart Order Routers high freq Venues The Logic of Financial Risk / 63

64 The Stack of Financial Algorithms low freq Collateral Trading high freq Inventory Management Algo Containers Trading Algos Smart Order Routers Venues we re here The Logic of Financial Risk / 64

65 The Stack of Financial Algorithms low freq Collateral Trading Inventory Management Algo Containers high freq Trading Algos Smart Order Routers Venues how do we get here? we re here The Logic of Financial Risk / 65

66 Formalized Financial Mathematics Assuming every order is a MARKET ORDER is ridiculous. We need new financial mathematics that takes the precise discrete market microstructure into account. The Logic of Financial Risk / 66

We need new financial mathematics that takes the precise discrete market

67 Formalized Financial Mathematics Assuming every order is a MARKET ORDER is ridiculous. We need new financial mathematics that takes the precise discrete market microstructure into account. Stochastic Control Stochastic Calculus Brownian Motion Wiener Processes Martingales The Logic of Financial Risk / 67

68 Conclusion Pressing need for: venues to be bullet-proof w.r.t. safety and fairness regulations matching logics to be formally described to regulators and market participants matching logics to be formally analysed w.r.t. precise encodings of regulatory directives financial mathematics (stochastic calculus) that takes precise discrete behaviour of matching logics into account this is a killer app for formal methods! The Logic of Financial Risk / 68

Algorithm Training Guide Q1 2017

Algorithm Training Guide Q1 2017 TIMED ORDER Key Parameters : START TIME - END TIME Behaviour Start Time represents the effective time at which an order will begin to become eligible to trade. If this