hidden treasure of high frequency dynamics

The hidden treasure of high frequency dynamics:

from intrinsic time to 12 new scaling laws

Richard Olsen

OLSENLiquidity Investing

Dec 2009 2The intrinsic time framework


Information content of tick data

Intrinsic time: event-based approach

12 new scaling laws

Outlook

Outline

Conclusion



You only see what you look at

Daily Data High-Frequency Data

1 day 1 25‘000

1 year 250 5‘000‘000

10 years 2‘500 50‘000‘000

100 years 25’000 500’000’000

Within a 24 hour time window, the world is more or less the same, so one day of tick data is more valuable than 100 years of daily data.

One day of high frequency tick by tick data is equivalent 100 years of daily data.



Tick data contains information

Risk capacity

Market maker

Price change



Market maker sends signals

Market maker

Buyer

Seller


OLSENLiquidity InvestingMarket moves are non-linear

price change

liquidationsmargin call

Large price trends are the result of cascading margin calls.

Example: recent USD upmoveis result of everyone getting it wrong....



Example: EUR_USD price action Friday 9th Jan 2009

Non-Farm Payroll data: 598‘000 jobs lost.



Example: trader action on Friday 9th Jan 2009

OrdersPositionsJan 9, 2009 12.30

Jan 9, 2009 13.30

Jan 9, 2009 14.30

Jan 9, 2009 12.30

Jan 9, 2009 13.30

Jan 9, 2009 14.30

Complimentary OANDA service, see http://fxlabs.oanda.com





Scaling laws

Outlook

Outline

Conclusion



EUR-USD, Nov 21 2008, daily return

A significant part of the activity is disregarded



EUR-USD, Nov 21 2008, daily return

Some activity is still disregarded, especially in the afternoon



EUR-USD, Nov 21 2008, 5 minutes return

0.3 %

1.2%

Is market time passing by at a constant pace?



In need of an event-based approach?

We have observed seasonailty and that time can speed up!

Why? The time series of prices is the result of the actions of all

traders

Can we address these issues within a top-down approach with a

unique notion of time? We believe this is close to impossible

Addtional units of time: intrinsic time

Price move occurences represent event and are unit of time

Important as the market is populated by a large variety of traders

sleeping at different time, with different profit objectives and

different risk appetite



Intrinsic time: an insight (1)

Physical timee.g. [hours]

1 2 3 4 5 6

Intrinsic time[events]

1 2 3 4

x

x

x

x



Intrinsic time: an insight (2)



Intrinsic time: pros and cons

Pros:

Full activity at a given price scales is observed

Seasonality and herding can be handled

Overshoot sections quantify the departure from the current price

level

Map how market participants see the market

Cope with the discountinuous nature of the market

Cons:

Relation to physical time and to price scales need to be

established

Volatility has to be defined





Scaling laws

Outlook

Outline

Conclusion



Existing scaling laws

Müller et al., J. Bank Finance, 1990: Mean absolute change of mid-price to time

Guillaume et al., Finance Stoch. 1997:Number of directional changes to thresholds



High-frequency FX data

A tick-by-tick data of 13 currency pairs:

AUD-JPY (15'286'858), AUD-USD (7'037'203),

CHF-JPY (17'081'987), GBP-CHF (27'141'146),

GBP-JPY (26'423'199), GBP-USD (13'918'523),

EUR-AUD (19'111'129), EUR-GBP (13'847'688),

EUR-CHF (9'912'921), EUR-JPY (22'594'396),

EUR-USD (13'093'081), USD-CHF (13'812'055),

USD-JPY (13'507'173).

From Dec 1 2002, and Dec 1 2007

A simple Gaussian random walk made of one million ticks at every

second:



1. Tick-count scaling law



Other laws at a glance (1)

2. Average yearly number of price

moves

3. Average maximal price move

during a time interval

4. Average duration of a price move

5. Average duration of a directional

change




Decomposition of total price move into directional-change and

overshoot

6-14. Leads to 9 additional scaling laws




15-17. Cumulative price moves

We find 12 independent new scaling laws.



All the scaling laws at a glance



The coastline of prices (1)

The coastline associated to a price scale is the sum of all price

moves of a given price scale.

Why is it important?

quantifies the profit potential

allows for active management of positions

A variation (transaction costs taken into account) of the total

move scaling law allows us to estimate its average length

0.05%: 1604%

0.1%: 1463%

1%: 161%

5%: 34.5%

The GRW shows up to a factor 2 times smaller coastline



The coastline of prices (2)

For 0.05% threshold, daily length: EUR-CHF 1.8%, AUD-JPY 9.1%

The coastline measures on average 6.4% per day

On average, daily a mean maximal move of 0.6% is observed

On average it takes 220 days to observe a 6.4% price move





Scaling laws

Outlook

Outline

Conclusion



Outlook (1)

Sparsity of data to explain macro trends

Treasure of tick by tick data: resource for model building

Comprehensive data repository of observed and synthetic data

Self-similar model building

Intrinsic time approach



Outlook (2)

Call to action: global economic crisis

Global information system

Collaboration

Data repository

Descriptive economics

Actual deliverables: real time services



Motivation


Scaling laws

Outlook

Outline

Conclusion



Finance as the next computer technology

· other industries have succeeded, why not economics and finance?

· human beings, complexity, unforeseen events.

· high frequency finance, new concepts, significant financial resouces.

· Yes, it is feasible · Thank you.



Directional change algorithm



Length and duration of overshoots

An interesting feature

also found by considering a binomial tree

And the time is twice in an overshoot than in a directional change



Comparison with a GRW

A GRW has strikingly similar properties than the average

properties of the market data

Noticable difference: average maximum price move is 8 times

larger than observed with the market data

Duration of price move

Exponent 0.500 when p=2

Average exponent 0.457 for market data, p=2

It is not 0.500 for any other law



Exploring the space of scaling law (1)

where

Simililarly

The average time for a price move to occur should be the yearly

number of seconds divided by the average number of price moves

indeed



Exploring the space of scaling law (2)

The empirical values lead to

Hence there is a tick to be expected every 279 seconds. The average

duration of price moves indicate an 0.02% price move every 258

seconds.

Scaling laws can be assembled to produce additional laws. For instance

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