Towards a Formal Modelling of Orders in Stock Trading Systems using Workflow Nets

MACSPro'2019 - Modeling and Analysis of Complex Systems and Processes, Vienna
21 - 23 March 2019

Julio Cesar Carrasquel, Irina Lomazova

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1. Towards a Formal Modelling of Order-driven Trading Systems using Petri Nets: A Multi-Agent Approach Julio C. Carrasquel Irina A. Lomazova National Research University Higher School of Economics Laboratory of Process-Aware Information Systems (PAIS)
2. Outline • Order-driven Trading Systems • Multi-Agent System (MAS) model • Agents and Petri Nets • Nested Petri Net model • Coloured Petri Net model • Research Directions
3. Order • An order o is a client instruction to trade a financial instrument. • Some attributes: ◦ side s ∈ { buy, sell } ◦ price per stock p ◦ quantity of stocks q • …we may consider other attributes such as: ◦ time of arrival ◦ validity ◦ display restrictions, quantity restrictions, ...
4. Order-driven Trading Systems • Order routing systems • Order books • Rule-based matching systems ◦ Order precedence rules ◦ Order matching • Order presentation systems and market data systems
5. Order-driven Trading Systems • Order routing systems • Order books • Rule-based matching systems ◦ Order precedence rules ◦ Order matching • Order presentation systems and market data systems
6. Order Precedence Rules - Arrival of orders time trader size price 10:01 Bea 3 20 10:08 Ben 2 20 10:15 Bif 4 market 10:18 Bob 2 20.1 10:29 Bud 7 19.8 time trader size price 10:05 Sam 2 20.1 10:08 Sol 1 19.8 10:10 Stu 5 20.1 10:20 Bob 2 20.1 Buy side arrivals Sell side arrivals
7. Order Precedence Rules - Ranking (Price-time policy) buyer size price price seller Bif 4 market 20.1 5 Stu Bob 2 20.1 2 Sam Bea 3 20.0 Ben 2 20.0 20.0 6 Sue Bud 7 19.8 1 Sol Order book
8. Matching Procedure buyer size price price seller Bif 4 → 3 market 20.1 5 Stu Bob 2 20.1 2 Sam Bea 3 20.0 Ben 2 20.0 20.0 6 Sue Bud 7 19.8 1 → 0 Sol Order book
9. Matching Procedure buyer size price price seller Bif 3 → 0 market 20.1 5 Stu Bob 2 20.1 2 Sam Bea 3 20.0 Ben 2 20.0 20.0 6 → 3 Sue Bud 7 19.8 Order book
10. Matching Procedure buyer size price price seller 20.1 5 Stu Bob 2 → 0 20.1 2 Sam Bea 3 20.0 Ben 2 20.0 20.0 3 → 1 Sue Bud 7 19.8 Order book
11. Matching Procedure buyer size price price seller 20.1 5 Stu 20.1 2 Sam Bea 3 → 2 20.0 Ben 2 20.0 20.0 1 → 0 Sue Bud 7 19.8 Order book
12. Matching Procedure buyer size price price seller 20.1 5 Stu 20.1 2 Sam Bea 2 20.0 Ben 2 20.0 Bud 7 19.8 Order book final state
13. Outline • Order-driven Trading Systems • Multi-Agent System (MAS) model • Agents and Petri Nets • Nested Petri Net model • Coloured Petri Net model • Research Directions
14. Multi-Agent System (MAS) model • Processes of the trading system → types of agents • (x) Request handler → Arrival of orders • (y) Order book handler → Ranking and matching • (z) Trade handler • An agent • Created upon request • Executes internal activities (either by initiative or reactivity) • Sends and receives messages from other agents (social behavior) • Terminated upon completion of its tasks
15. Agents and Petri Nets verify order receive order a 1 a 2 a 3 a 4 reject order place in book Agent x 1 o 1 = (Bif ,market ,4,buy)
16. Agents and Petri Nets verify order receive order a 1 a 2 a 3 a 4 reject order place in book Agent x 1 o 1 = (Bif ,market ,4,buy) a 4 rank sell order receive buy order receive sell order rank buy order notify match replace cancel expire notify order filled notify order partially filled b 1 b 2 b 3 b 4 b 5 b 6 b 7 b 8 b 9 b 10 Agent y 1
17. Agents and Petri Nets rank sell order receive buy order receive sell order rank buy order notify match replace cancel expire notify order filled notify order partially filled b 1 b 2 b 3 b 4 b 5 b 6 b 7 b 8 b 9 b 10 Agent y 1 handling a buy order o 1 rank sell order receive buy order receive sell order rank buy order notify match replace cancel expire notify order filled notify order partially filled b 1 b 2 b 3 b 4 b 5 b 6 b 7 b 8 b 9 b 10 c 1 both orders filled c 2 c 3 order filled and other one partially filled c 5 notify trade c 4 Agent z 1 handling(o 1, o 2 ) Agent y 2 handling a sell order o 2
18. Nested Petri Net model • Tokens can be Petri Net themselves • System net - an environment describing ◦ Creation and termination of system processes (agents) ◦ Communication interfaces (via vertical synchronization steps) ◦ Shared execution constraints between multiple agents, I.e, matching process. • Focus on the control-flow perspective and communication interfaces
19. Nested Petri Net model – system net (fragment) Invoke request handler reject order t 2 o o request handlers (x ,o) (y ,o) order book handlers place in book t 1 receive order a 3 request handlers serving orders order book handlers serving orders a 4 (x ,o) received orders (x ,o) verify order receive order a 1 a 2 a 3 a 4 reject order place in book Pair (x 1, o 1 ) indicating that agent x 1 handles o 1 agent net x 1 vertical synchronization labels System net (fragment)
20. Nested Petri Net model – system net (fragment) cancel (y ,o) expire order book handlers replace (y ,o) (y ,o) (y ,o) place in book (y ,o) notify match (y ,o) t 7 2 2 (y ,o) notify order filled notify order partially filled (y ,o) (y ,o) order book handlers serving orders enable next matching a 4 b 5 b 6 b 7 b 8 b 9 b 10 t 3 orders matched pending Pair (y 1, o 1 ) Pair (y 2, o 2 )
21. Nested Petri Net model – system net (fragment) (z,2⋅o) invoke matching handler trade handlers 2⋅(y ,o) c 4 notify trade (z,2⋅o) 2⋅o send trade to client 2⋅o terminate matching handler z c 3 c 2 both orders fulfilled order fulfilled and other one partially fulfilled 2⋅o o o o o o notify order filled notify order partially filled (y ,o) b 9 b 10 c 5 t 4 t 5 trade handlers running orders matched pending 2⋅o
22. Nested Petri Net model – system net (complete) Invoke request handler cancel reject order t 2 o o (x ,o) (y ,o) expire order book handlers replace o (y ,o) (y ,o) (y ,o) place in book (y ,o) notify match (y ,o) t 7 (z,2⋅o) invoke matching handler trade handlers 2⋅(y ,o) c 4 notify trade (z,2⋅o) 2⋅o send trade to client 2⋅o terminate matching handler z c 3 c 2 both orders fulfilled order fulfilled and other one partially fulfilled 2⋅o o o o o o 2 2 t 1 (y ,o) notify order fulfilled notify order partially fulfilled (y ,o) (y ,o) receive order request handlers serving orders order book handlers serving orders enable next matching a 4 (x ,o) b 5 b 6 b 7 b 8 b 9 b 10 c 5 t 3 t 4 t 5 trade handlers running orders matched pending received orders (x ,o) 2⋅o request handlers a 3
23. Coloured Petri Net (CPN) model • Tokens have data types (colors) associated. colset SIDE = with buy | sell colset ORDER = product STRING * INT * INT * SIDE colset ORDER_PAIR = product ORDER * ORDER colset ORDER_BOOK = list ORDER • An order book is modeled as two tokens (of type ORDER_BOOK) • Representing the buy side and the sell side.
24. Coloured Petri Net (CPN) model – modelling MAS • CPN may not be a convenient representation of Multi-Agent Systems • Conceived approach → hierarchical CPN with sub-pages • System net (environment) → Model top page • Each sub-page → structure of a kind of agent (process) • Current point of execution of an agent → a variable in the sub-page • We loss the notion of mobility
25. Coloured Petri Net (CPN) model – system net Sub-page describing the behavior of an agent encapsulated on a substitution transition
26. Coloured Petri Net (CPN) model – order book handler example agent y 1 handling o BEN agent y 3 handling o BIF agent y 4 handling o SAM
27. Coloured Petri Net (CPN) model – order book handler example rank sell order receive buy order receive sell order rank buy order notify match replace cancel expire notify order filled notify order partially filled b 1 b 2 b 3 b 4 b 5 b 6 b 7 b 8 b 9 b 10 rank sell order receive buy order receive sell order rank buy order notify match replace cancel expire notify order filled notify order partially filled b 1 b 2 b 3 b 4 b 5 b 6 b 7 b 8 b 9 b 10 rank sell order receive buy order receive sell order rank buy order notify match replace cancel expire notify order filled notify order partially filled b 1 b 2 b 3 b 4 b 5 b 6 b 7 b 8 b 9 b 10 agent y 1 handling o BEN agent y 3 handling o BIF agent y 4 handling o SAM
28. Coloured Petri Net (CPN) model – Order precedence rules fun buy_rank (i, p, q, s) [ ] = [(i, p, q, s)] // o = (i, p, q, s) | buy_rank (i, p, q, s) ( (i2, p2, q2, s2)::list ) = if p > p2 then // ranking according to price (i, p, q, s) :: (i, p2, q2, s2) :: list else (i2, p2, q2, s2) :: (buy_rank (i, p, q, s) list) • Use of a CPN ML function on the input arc of the place for orders to manipulate conveniently the list when inserting a new order.
29. Coloured Petri Net (CPN) model – Guards • Use of a boolean function as an additional constraint for a transition to be enabled. • Thus, it imposes an additional condition for an activity execution based on the data. Guard function for enabling matching
30. Outline • Order-driven Trading Systems • Multi-Agent System (MAS) model • Agents and Petri Nets • Nested Petri Net model • Coloured Petri Net model • Research Directions
31. Research Directions MODELLING stock trading software systems simulation event logs record events. i.e. messages, orders, transactions, etc. CONFORMANCE CHECKING verification of behavioral properties PERFORMANCE ANALYSIS a b c d system net (agent society) stock exchange “world” brokers, orders, trades,... supports/controls a c d a b c d a b c d Petri-net-based models Multi-agent system (MAS) approach processes (agents)
32. Research Directions – A possible simulation environment