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

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)

View Slide

Outline
● Order-driven Trading Systems
● Multi-Agent System (MAS) model
●
Agents and Petri Nets
●
Nested Petri Net model
●
Coloured Petri Net model
● Research Directions

View Slide

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, ...

View Slide

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

View Slide

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

View Slide

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

View Slide

Matching Procedure
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

View Slide

Matching Procedure
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

View Slide

Matching Procedure
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

View Slide

Matching Procedure
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

View Slide

Matching Procedure
20.1 5 Stu
20.1 2 Sam
Bea 2 20.0
Ben 2 20.0
Bud 7 19.8
Order book final state

View Slide

Outline
●
●
●

View Slide

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

View Slide

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)

View Slide

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

View Slide

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

View Slide

● 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

View Slide

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)

View Slide

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
)

View Slide

(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

View Slide

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

View Slide

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.

View Slide

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

View Slide

Coloured Petri Net (CPN) model – system net
Sub-page describing
the behavior of an
agent encapsulated
on a substitution
transition

View Slide

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

View Slide

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

View Slide

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.

View Slide

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

View Slide

Outline
●
●
●

View Slide

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)

View Slide

Research Directions – A possible simulation environment

View Slide

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

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

Exactpro
PRO

More Decks by Exactpro

Other Decks in Research

Featured

Transcript

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

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

Exactpro PRO

More Decks by Exactpro

Other Decks in Research

Featured

Transcript

Exactpro
PRO