Algorithmic Trading: An Algorithmic Trading: An Overview of Applications And Overview of Applications And

Models.Models.Ekaterina Kochieva

Gautam Mitra

Cormac Lucas

Contents

Introduction Stock exchange mechanism Models for trade scheduling

– Background– Basic models

References

Introduction

Until recently, most of financial research focused on the investment decisions.

There was a missing part of investment cycle — execution of investment decisions.

More over, many investment optimization models assume zero execution cost. But in reality it is not true.

Ignoring this fact may lead to significant mistake in estimating investment returns.

Stock exchange mechanism

Overview of stock exchanges The main stock exchanges in the world include: America

– American Stock Exchange– NASDAQ– New York Stock Exchange– São Paulo Stock Exchange

Europe– Euronext– Frankfurt Stock Exchange– London Stock Exchange– Madrid Stock Exchange– Milan Stock Exchange– Zurich Stock Exchange– Stockholm Stock Exchange

Overview of stock exchanges

Australia/Asia/Africa– Australian Stock Exchange

– Bombay Stock Exchange

– Hong Kong Stock Exchange

– Johannesburg Securities Exchange

– Korea Stock Exchange

– Shanghai Stock Exchange

– Taiwan Stock Exchange

– Tokyo Stock Exchange

– Toronto Stock Exchange

Listing requirements

LSE — main market has requirements for a minimum market capitalization of £700,000, three years of audited financial statements, minimum public float of 25 % and sufficient working capital for at least

12 months from the date of listing NASDAQ — to be listed a company must have issued at least 1.25

million shares of stock worth at least $70 million and must have earned more than $11 million over the last three years

NYSE — a company must have issued at least a million shares of stock worth $100 million and must have earned more than $10 million over the last three years

Participants Broker — an individual or firm which operates between a buyer and a seller

and usually charge a commission. For most products a licence is required.

Dealer — an individual or firm which buys and sells for its own account.

Broker/dealer — an individual or firm buying and selling for itself and others. A registration is required.

Principal — a role of broker/dealer when buying or selling securities for its own account.

Market maker — a brokerage or bank that maintains a firm bid and ask price in a given security by standing ready, willing, and able to buy or sell at publicly quoted prices (called making a market). These firms display bid and offer prices for specific numbers of specific securities, and if these prices are met, they will immediately buy for or sell from their own accounts.

Specialist — a stock exchange member who makes a market for certain exchange-traded securities, maintaining an inventory of those securities and standing ready to buy and sell shares as necessary to maintain an orderly market for those shares. Can be an individual, partnership, corporation or group of firms.

Prototypical trading systems Call (periodic) auction — selling stocks by bid at intervals

throughout the day. The orders are stored for execution at a single market clearing price.

Continuous auction — buyers enter competitive bids and sellers place competitive offers simultaneously. Continuous, since orders are executed upon arrival.

Dealership market — trading occur between principals buying and selling to their own accounts. Firm price quotations are available prior to order submission.

Auction markets are concentrated and order-driven Dealership markets are fragmented and quote-driven

Examples

NYSE — opens with a periodic auction market and then

switches to a continuous auction. Same for Tokyo Stock Exchange.

NASDAQ and International Stock Exchange (London) are quote-driven systems (continuous dealership market).

Examples

Euronext Paris — the market is segmented into a number of different groups of stocks based on size and liquidity. The trading mechanisms vary depending on the segment.

Euronext 100, Next 150 ,CAC40 indices and stocks which have more than 2,500 order book transactions per year — continuous auction.

Other stocks — call auction twice a day.

Order types

Market order — immediate execution at the best price available when the order reaches the marketplace

Limit order — to execute a transaction only at a specified price (the limit) or better

Stop order Good till cancelled Fill-or-kill All or None Day order

Limit order book

A register for limit buy orders and a registry for limit sell orders.

Limit orders are queued for execution against incoming market orders using price then time priority rules.

Transparency: how much top orders can be viewed More transparent order book allows to see what is

happening in the market and make more accurate forecasts

Limit order book

0

500

1000

1500

2000

49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5

BidAsk

Cumulative Order Book

00.05

0.10.150.2

0.250.3

0.350.4

4,2003,5002,5001,5005000 5001,5002,5003,5004,500

Size

Avg

. Pri

ce (

$/S

har

e) Cum. Bid

Cum. Ask

Example

Euronext Paris — high transparency market:

Brokers observe the full limit book at all times

Other investors can observe the volume of orders available at the five best prices

Placing orders: How does it work?

Exchange

Electronic Communications Network

Market Maker

Firm Internalizes Order

Internet

order

Phone

order

Electronic Communication Network

ECN is a computer system that facilitates trading of financial products outside of stock exchanges. The primary products that are traded on ECNs are stocks and currencies.

In order to trade with an ECN, one must be a subscriber. ECN subscribers can enter limit orders into the ECN, usually via a custom computer terminal or a direct dial-up. The ECN will post those orders on the system for other subscribers to view. The ECN will then match contra-side orders for execution.

Generally, the buyer and seller are anonymous, with the trade execution reports listing the ECN as the party.

Principal bid

A transaction where a broker/dealer provide an investor with guaranteed execution of the trade list at the market prices at a specific point in time.

All timing risk is transferred to broker/dealers. Investors are charged a premium for this.

Blind bid — investor provides only trade list statistics. Than broker/dealer defines the price.

The spread between Principal and Agency

Investor Cost Implications

Agency ExecutionPrincipal Bid Transaction

Trading CostsComission Yes NoPrice Appreciation Yes NoMarket Impact Yes NoTiming Risk Yes NoOpportunity Cost Yes NoPremium Fee No YesKnown Price No YesGuaranteed Completion No YesTrading Cost Forecast Distribution of Cost Single Value Estimate

Models for trade Scheduling

1. Background

Trading cost iceberg

Traders dilemma

Market impact is a decreasing function with time and volume.

Timing risk is an increasing function with time and volume.

So, trading too aggressively will cause investors to incur high market impact cost and low timing risk. Trading too passively means having low market impact cost but high timing risk.

Potential execution strategies

Min cost in presence of risk

Balance trade off between cost and risk

Max probability of price improvement

*k

k

R)R(x s.t.

)φ(xMin

)R(xλ)φ(xMin kk

*k L))(xProb(Max

Constraints

Completion

Monotony (shrinking portfolio)

Participation rate

Cash balance

ij

ij Xx

1 ijij rr

ijij

ij

vx

x

maxmin DcashD j

Market impact

Market impact is primarily caused by: Supply-demand imbalance (liquidity needs) Information leakage

Market impact could be Temporary — occurs when the order is released but does

not alter market’s long-term outlook caused by liquidity demand and immediacy requirements.

Permanent — long-term change in price caused by an order.

Market impact bubble

Time

Pri

ce

Temporary market impact

Time

Pri

ce

Permanent market impact

Time

Pri

ce

Long-lived Temporary MI

Time

Pri

ce

Timing risk. Opportunity risk.

Timing risk grows from the uncertainty surrounding trading cost estimates. It includes price volatility and instability in volume profiles during a day.

Opportunity risk is of not being able to implement investment decision in full. It is caused by insufficient stock liquidity or unfavourable price movement.

Models for trade Scheduling

2. Basic models

Bertsimas and Lo

Fixed blocks of shares s=[s1,…,sn]’

Fixed finite number of periods T Set of price dynamics: Price = “no-impact” price + linear impact function

Find optimal sequence of trade to minimize expected transaction cost

ttt pp ~

Further improvements

Almgren and Chriss (2000) — permanent and temporary impact, efficient frontier of execution.

Almgren (2003) — non-linear impact function.

Malamut (2002) — instantaneous market impact: pre-calculated aggregate impact value to each period.

Further improvements

Kissel and Glantz(2003) — ETF used to define best trading strategies. Concept of a capital trade line (CTL) for mixed trading strategies (agency versus principal bid).

Obizhaeva and Wang (2005) — adding supply/demand dynamics. Model includes discrete and continuous trading.

Engle and Ferstenberg (2006) — integration of portfolio decision and the execution decision. Hedging the trading risk.

References

Almgren, R. and N. Chriss, 2000, Optimal Execution of Portfolio Transactions. Journal of Risk 3, 5-39

Almgren, R., 2003, Optimal Execution with Nonlinear Impact Functions and Trading-enhanced Risk. Applied Mathematical Finance 10, 1-18

Bertsimas, D. and A. W. Lo, 1998, Optimal Control of Execution Costs. J. Financial Markets 1, 1-50.

Malamut R., 2002, Multi-Period Optimization Techniques for trade Scheduling, QWAFAFEW presentation

Obizhaeva, A. and J. Wang, 2005, Optimal Trading Strategy and Supply/Demand dynamics, NBER working paper

Engle, R., and R. Ferstenberg, 2006, Execution Risk, NBER working paper

References

Kissel, R. and M. Glantz, 2003, Optimal Trading Strategies. Amacom

Bennouri, M., 2005, Auction versus Dealership Markets Madhavan, A., 1992, trading Mechanisms in Securities Markets.

The Journal of Finance, vol. XLVII, 2 Comerton-Forde, C. and A. Frino, 2004,The Impact of Limit

Order Anonymity on Market Liquidity. SIRCA Working Paper

Thank you!