Continuous double auction (zero-intelligence order book)

Field: economics · Zoo name: order_book · Module: modelly.zoo.order_book.model

A limit order book on an integer price grid, fed by random order flow, as in the zero-intelligence model of Farmer, Patelli and Zovko. With probabilities in proportion to their rates, an event is a market buy or sell, which takes one unit at the best opposite price; a limit buy or sell, which rests at a price drawn uniformly 1 .. window ticks inside the opposite best quote, so it never crosses; or the cancellation of a uniformly random resting order. No trader has a strategy, yet the prices show some of the stylised facts of real markets.

How it is written

The book is two numpy arrays of depth per tick, bids and asks; the best quotes are the last and first non-empty levels. Each event draws its kind from the six rates (model.rates()), and a cancellation picks its order in proportion to depth with one cumsum and searchsorted. An event that would empty a side becomes a limit order on that side. A step is events events; the mid price and the spread are collected after each step.

from modelly.zoo.order_book.model import OrderBook, OrderBookScenario

model = OrderBook(OrderBookScenario(rng=42))
model.run()
model.best_bid(), model.best_ask()
model.returns()  # log returns of the mid price, step to step
model.datacollector.get_model_vars_dataframe()  # mid price and spread per step

Parameter	Default	Meaning
ticks	1000	number of price levels
window	20	limit orders rest 1 .. window ticks from the opposite best quote
market_rate	0.3	rate of market orders, both sides together
limit_rate	1.0	rate of limit orders, both sides together
cancel_rate	0.005	rate of cancellation per resting order
initial_depth	2	orders per level in the window levels of each side at start
events	10	order events per step
steps	2000	run length of run()

Validation

Real returns have fat tails: their excess kurtosis is positive (Cont, 2001). tests/zoo/test_order_book.py runs 2,000 steps with three seeds and checks the excess kurtosis of the mid-price returns is above five times sqrt(24 / n), its standard error if the returns were normal; it is about thirty standard errors in practice. It also checks the spread is always at least one tick, that aggressive market orders never empty a side of a one-order book, and that the same seed gives the same price path.

References

• Farmer, J. D., Patelli, P. and Zovko, I. I. (2005). The predictive power of zero intelligence in financial markets. PNAS, 102(6), 2254-2259.

• Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance, 1, 223-236.

Start a project from it with modelly zoo copy order_book my_market.