Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research...
-
Upload
meaghan-grist -
Category
Documents
-
view
214 -
download
0
Transcript of Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research...
![Page 1: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/1.jpg)
Market forces I: Price Impact
J. Doyne FarmerSanta Fe InstituteLa Sapienza, 8 marzo
Research supported by Barclays Bank
![Page 2: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/2.jpg)
Market forces
• Supply and demand are in a loose sense like forces in physics.
• What determines supply and demand curves?
• Are they the best approach?– Market dynamics– Observability problems
![Page 3: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/3.jpg)
Standard approach to determining supply and
demand• Assume agents selfishly maximize utility• Make an assumption about optimization algorithm agents use:– Standard: Perfect rationality– “Behavioral”: One rational, others noise
• Make an assumption about markets– Market clearing– Price taking
• Simplifications: (no production, no inter-temporal reasoning, …
• Economy is at a Nash equilibrium• Research since 1980: Modify assumptions
![Page 4: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/4.jpg)
What drives changes in prices?
• Standard view: expectations about future earnings driven by new information– new information alters expected earnings and changes fundamental value
– prices quickly adjust to new fundamental value
– prices are unpredictable because new information is by definition random
![Page 5: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/5.jpg)
Rationality?
![Page 6: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/6.jpg)
Elliot waves
![Page 7: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/7.jpg)
Fibonnaci predicts social trends!
![Page 8: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/8.jpg)
Overfitting
![Page 9: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/9.jpg)
Problems with standard view
• Far too much trading (> 50 x GDP)• Volatility is not random
– size of price changes is correlated in time
• Many price changes not information driven
• Prices deviate from fundamental values• Prices have exploitable patterns
– weak, difficult to find, but not zero
![Page 10: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/10.jpg)
Volatility
![Page 11: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/11.jpg)
Problems with standard view
• Far too much trading (> 50 x GDP)• Volatility is not random
– size of price changes is correlated in time
• Many price changes not information driven
• Prices deviate from fundamental values• Prices have exploitable patterns
– weak, difficult to find, but not zero
![Page 12: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/12.jpg)
![Page 13: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/13.jpg)
Problems with standard view
• Far too much trading (> 50 x GDP)• Volatility is not random
– size of price changes is correlated in time
• Many price changes not information driven
• Prices deviate from fundamental values• Prices have exploitable patterns
– weak, difficult to find, but not zero
![Page 14: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/14.jpg)
Prices do not match fundamental values
Comparison of pseudo S&P index (solid) to fundamental valueestimate based on dividends (dashed)
![Page 15: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/15.jpg)
![Page 16: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/16.jpg)
Problems with standard view
• Far too much trading (> 50 x GDP)• Volatility is not random
– size of price changes is correlated in time
• Many price changes not information driven
• Prices deviate from fundamental values• Prices have exploitable patterns
– weak, difficult to find, but not zero
![Page 17: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/17.jpg)
Prediction Company (cofounded in 1991 with Norman
Packard)
• Does fully automated proprietary trading in international stock markets under profit sharing relationship relationship with United Bank of Switzerland (Warburg Dillon Read)
• “Cerebellar” approach to market forecasting– empirically search for patterns in historical data – keys are feature extraction, central limit theorem– little understanding of origin of patterns– relies on abundant past data, stationary conditions
• 50 employees.
![Page 18: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/18.jpg)
![Page 19: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/19.jpg)
Profits?
• Finding a persistent pattern doesn’t mean you can make an infinite amount of money.– (reason is market impact)– depends on timescale
• How much you can make is sensitively dependent on market impact
![Page 20: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/20.jpg)
![Page 21: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/21.jpg)
Price Impact(also called market
impact)• Response of price to receipt of an order• Related to derivative of aggregate demand function = demand - supply.
• With a few caveats, has the important advantage of being directly measurable.– No information about price level, only price change
€
p = D(q)dp
dq=
dD
dq
![Page 22: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/22.jpg)
Price impact vs. order size for different market
capitalizations
With Fabrizio Lillo and Rosario Mantegna
![Page 23: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/23.jpg)
Data collapse
• Use market capitalization C as liquidity proxy
• Find empirically to minimize variance
γδ yCy
C
xx →→
δγ,
![Page 24: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/24.jpg)
Master price impact curve
![Page 25: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/25.jpg)
Zero intelligence model of price formation
• Assume agents place orders to buy or sell, make cancellations, “at random”– make everything a Poisson process– make distributions and rates uniform– equal for buying and selling.
• What are properties of resulting prices?– Dimensional analysis (price, time, shares)
– Scaling laws for spread and volatility in terms of parameters of order flow
![Page 26: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/26.jpg)
Giulia Iori
Giulia Iori Eric Smith
Laszlo Gillemot Supriya Krishnamurthy
Marcus Daniels
Continuous doubleauction model collaborators
![Page 27: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/27.jpg)
Continuous double auctionContinuous: Market operates asynchronously
Double: Price adjustment in orders both to buy and to sellExecution priority: • Lower priced sell orders or higher priced buy orders have
priority• First order placed has priority when multiple orders have
same price.
price ($)
SPREAD
PRIORITY
PRIORITY
(BEST) BID
(BEST) ASK
VOLUME
SELL
BU
Y
VO
LUM
E
LIMIT ORDERS
![Page 28: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/28.jpg)
price ($)
BID
ASK
VO
LUM
E
Patient trading• Patient traders place non-marketable
limit orders that do not lead to an immediate transaction
• Non-marketable limit orders accumulate
• Limit order book is a storage device
NEW ASK
Limit Order
BUY / SELL
# OF SHARES
LIMIT PRICE
Patient trading• Patient traders place non-
marketable limit orders that do not lead to an immediate transaction
• Non-marketable limit orders accumulate
![Page 29: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/29.jpg)
price ($)
Impatient trading
Market order:• An order to buy or sell up to a given
volume• No limit price is defined• Executed immediately• Often causes unfavorable price impact
Market Order
BUY / SELL
# OF SHARES
BID
ASK
BID
NEW ASK
VO
LUM
E
Impatient trading
![Page 30: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/30.jpg)
Order cancellation
price ($)
Limit order cancellations: • Limit orders can be cancelled by the owner • Market defined expiration
price ($)price ($)
VO
LUM
E
![Page 31: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/31.jpg)
ZI model (Unrealistic but somewhat tractable)
Limit order arrival: Poisson process in time & price;
Market order arrival: Poisson process in time; Cancellation: random in time (like radioactive decay); δ
Separate processes for buying and selling, with same parameters.
Depth profile np,t: Number of shares in limit order book at price p, time t.
BID
SELL LIMIT ORDERS
AS
K
BUY LIMIT ORDERS
SELL MARKETORDERS
BUY MARKET ORDERS
),( tpΩ
p0
),( tpn
![Page 32: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/32.jpg)
Parameters of model
€
=limit order rate (S/PT)μ = market order rate (S/T)δ = order cancellation rate (1/T)σ = typical order size (S)
dp = tick size (P)
Order flow rates
Discreteness parameters
Three fundamental dimensional quantities:shares S, price P, time T
![Page 33: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/33.jpg)
Price impact from ZI modelReal data shows less variation with epsilon
than theory predicts
dots 002.0
dashed 02.0
solid 2.0
======
εεε
![Page 34: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/34.jpg)
Market impact fn- non dim units
Market impact function(non-dimensional units)
€
ˆ N =Nδ
μ
€
Δˆ p =Δpα
μ
![Page 35: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/35.jpg)
Testing prediction of spread
• Equation of state from mean field theory
€
E[s] = μ
αf (
σδ
μ)
![Page 36: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/36.jpg)
From top 10 Russian jokes, Oct. 23, 2003
с сайта "Немецкая волна"http://www.dw-world.de/russian/0,3367,2212_A_985770_1_A,00.htmlУченые-экономисты давно стараются понять закономерности, которымподчиняются биржевые курсы, и используют для этого математическиемодели. На протяжении многих десятилетий такие модели исходили из
представлений о брокерах как об аналитиках с выдающимися умственнымиспособностями, обладающих исчерпывающей информацией о рынке и
действующих исключительно рационально. Однако удовлетворительно описатьреальные изменения биржевых курсов эти модели оказались не в состоянии.
Значительно успешнее справляется с этой задачей новая модель,предложенная Дойном Фармером (J. Doyne Farmer), сотрудником ИнститутаСанта-Фе в штате Нью-Мексико. Она базируется на предположении, что
брокеры Ц полные Ђидиотыї, действующие совершенно случайно и к тому желишенные какой бы то ни было информации. Сравнив данные, рассчитанные наоснове этой модели, с реальными курсами лондонской фондовой биржи запериод с 1998-го по 2000-й годы, ученые выявили очень высокую степень
совпадения
![Page 37: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/37.jpg)
Price impact on longer timescales
• Aggregate signed volumes for N successive transactions.
• Aggregate signed price return for N successive transactions.
• Vary N.• Normalize x and y axis according to mean value of absolute aggregate signed volume.
![Page 38: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/38.jpg)
![Page 39: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/39.jpg)
Price impact on longer time scales
![Page 40: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/40.jpg)
![Page 41: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/41.jpg)
![Page 42: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/42.jpg)
Statistical model
![Page 43: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/43.jpg)
Decomposition of price impact
Price impact has two parts:• Mechanical (direct) impact
– When an order enters the book, it alters the state of the book, which alters future prices even if nothing else changes.
• Indirect impact– Placement of the order may alter placement of future orders -- this measures interaction of agents.
– Change can be due to direct impact or to other factors (e.g. direct observation of order placement)
Is it possible to separate direct and indirect impacts?
![Page 44: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/44.jpg)
Measurement of direct impact
• Any allowed sequence of orders and cancellations yields a unique price series– Cannot cancel an order that doesn’t exist
• Can remove an order and then compute new series of prices– Can also partially remove an order– Can add orders
• Difference in prices measures mechanical (direct) impact
![Page 45: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/45.jpg)
![Page 46: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/46.jpg)
![Page 47: Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.](https://reader035.fdocuments.us/reader035/viewer/2022070306/55190d0055034642428b47cb/html5/thumbnails/47.jpg)