Although the Fixed-Income market overall still lacks liquidity and overall transparency, the Eurodollar futures are a very liquid and accessible portion of it. Eurodollar market is defined by a set of key features: pro-rata matching, large tick size, overlapping and highly correlated set of contracts, hidden implied liquidity and sticky price quotes. We will describe methodologies suitable for dealing with the market's complexity, making the case that high-frequency market-making, alpha trading & algorithmic execution need to be linked closely to achieve continued success.

1. Quantitative Trading in
the Eurodollar Futures
Market
Edith Mandel
Greenwich Street Advisors, LLC
QuantCon 2016

2. Fixed Income Market in Transition
Edith Mandel | Greenwich Street Advisors, LLC
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Eurodollars

3. Introduction
— Eurodollar Futures Market Overview
— Order Matching: Pro-Rata with ‘Top’
— Optimal Order Sizing & Risk Management
— Implied & Hidden Liquidity
— Solving for Additional Liquidity to Improve
Execution
— Historical & Cross-Sectional Dynamics
— Liquidity Provision with State Space Models
— Applications of Term Structure Models
Edith Mandel | Greenwich Street Advisors, LLC
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4. Eurodollar Market Overview (I)
— Highly liquid market (~2mm contracts trade daily)
not well-known to investors
— Cash-settled bets on future level of LIBOR rates
— U7@9900 -> LIBOR @1% as of Sep-2017
— Large universe of contracts:
— Outrights (quarterly to 10 yrs & 4 front serials)
— Combos (~1000)
— Spreads/Butterflies/Condors
— H0-U0 @13.50 -> Buy Mar-2020, Sell Sep-2020
— Packs/Bundles
— Large tick size (0.25bp for Packs/Bundles, 0.5bp
for all other contracts)
Edith Mandel | Greenwich Street Advisors, LLC
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5. Eurodollar Market Overview (II)
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6. Order Matching Algorithm
— Eurodollars use ‘Allocation’ method (Pro-Rata with Top)
— Profound impact on market microstructure
— Logic inherited from pit trading days
— Large limit orders are encouraged
— Low volatility products
— Allocation Example:
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7. Trading in Pro-Rata Markets (I)
— Implications of Pro-Rata:
— Significant order over-sizing
— Thick order books
— Actual bid-offer is @tick size in ~99% of trades
— Order cancellation rates >95%
— Ratio of available size to average trade size is ~200
— Risk of over-trading by liquidity providers
— Risk of losses due to overfills followed by panic
unwinds
Edith Mandel | Greenwich Street Advisors, LLC
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8. Trading in Pro-Rata Markets (II)
Thick Order Books
Multi-tick moves in the
span of several minutes
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U6
Z6
H7
M7

9. Trading in Pro-Rata Markets (III)
— Field & Large (2012) developed a model for optimal
limit order sizing
— min z(F)=E[[Fi(F) – S*]|Q,PM,U]2
— S* is desired position size
— Fi is the size allocated to i-th liquidity provider
— Q is overall market depth
— PM is a distribution of market order size
— U is risk tolerance function
— Offered depth is bounded due to a substantial risk of
over-trading in the Pro-Rata markets
— Risk of over-trading can be minimized, but not avoided
Edith Mandel | Greenwich Street Advisors, LLC
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10. Eurodollar Market: Implied Liquidity
First Generation Implied
— Example:
— Many ways to buy U7, given
visible liquidity:
— U7
— Z7 + [U7 – Z7]
— [U7-Z7-H8] +[Z7-H8]+Z7
— -------
— CME computes and
disseminates first generation
implied liquidity
— Latencies are likely
Implied From Implied &
Hidden Liquidity
— [Visible liquidity, First
generation implied] ->
Second generation implied
— Example of hidden
liquidity:
— [U7-Z7-H8] -[U7-H8] imply
liquidity for 2 lots of Z7
— This information is not
disseminated by CME
— Sourcing addition liquidity
can lower execution costs
Edith Mandel | Greenwich Street Advisors, LLC
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11. Computing Hidden Liquidity (I)
— Solving for hidden liquidity fits into Integer Linear
Programming (ILP) framework
— Example:
— Visible best offer for [Z7-H8] is 1100@5.5
— Can we improve on this offer price, using all available
liquidity, and for how much size? Can we find more
size at the same price point?
— ILP formulation:
— Find x (with non-negative integer elements) that
minimizes cTx, subject to constraints
— Ax=b
Edith Mandel | Greenwich Street Advisors, LLC
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12. Computing Hidden Liquidity (II)
— Practical Considerations:
— Speed of ILP: using modifications of simplex instead
— Instant price improvement is common, but for
modest size
— Most useful for gradual execution of large trades
— Need to embed price & size constraints
— High profitability in periods of market stress
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13. Eurodollar Market: Dynamics
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— Strong yield curve effect, high correlations between
the contracts
— Low asset price volatility vs. large tick size
— Price quotes are sticky: tick size is too large for bid
and ask to move
— High value-added in limit orders filled
— Market activity occurs in bursts, inventory is often
difficult to turn around
— Regular order book imbalance is magnified by Pro-
Rata effects

14. Eurodollar Market: Sparse Activity
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15. GEM7 after FOMC minutes release
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16. Market-Making Approach (I)
— Order book-based signal (‘Micro Price’) cannot
be ignored, but it’s insufficient
— Need for a Mid-Frequency forecast
— Term structure effect
— Holding inventory
— Trading activity is sparse
Edith Mandel | Greenwich Street Advisors, LLC
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17. Market-Making Approach (II)
— Kalman filter is used to improve upon a Micro Price
forecast
— Measurement equation links latent state variables to
observable data (Trade prices & Mid prices)
— State transition equation is provided by Term Structure
Models (TSM) or historical Factor Models (Cointegration)
— Market-maker wants to bid @forecast - f1(β) and sell
@forecast + f2(β), where βis a contribution to portfolio
risk
— Need a risk model to quantify it
— Optimal portfolio target is constructed given existing
inventory, forecasts, risk tolerance and assumptions
about fills and transaction costs
Edith Mandel | Greenwich Street Advisors, LLC
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18. TSM in Quant Trading
• Low-dimensional Term Structure Models (TSM)
capture rate market dynamics well
• Forecasting capabilities
• TSM links cross-sectional and time-series behavior
of rates in an internally consistent way
• TSM provides a risk model
• TSM is a source of a state-space transition
equation used in a Kalman filter framework
• Can be used in conjunction with historical factor
models
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19. Example: Affine Term Structure
Model (TSM)
• Realistic dynamics of the
yield curve:
• Multi-dimensional state
vector with non-zero
correlations
• Negligible (or non-existent)
probabilities of negative
long rates
• Ability to produce
deterministic and stochastic
skew and smile in the model
r(t) =!(t)+"T
X(t)
dX(t) = {µQ
! KQ
X(t)}dt + "S(t)dWQ
(t)
dX(t),dX(t) = "S(t){"S(t)}T
S(t) is diagonal with elements:
Sii (t) = H0i (t)+ H1i
T
(t)X(t)
Edith Mandel | Greenwich Street Advisors, LLC
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20. Properties Of Affine TSM
• Tractable pricing and risk analytics for bonds,
swaps, bond futures, Eurodollars and options
• Model can be used in the Equilibrium and the
Arbitrage-Free form
• Heston, Vasicek and CIR models are all examples of
Affine TSM
• We assume normal transition density over small
time intervals, using first 2 moments of the non-
central χ2-squared distribution
• Gaussian version of Affine TSM is suitable in some
applications
Edith Mandel | Greenwich Street Advisors, LLC
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21. Modeling Eurodollars with Affine
TSM
§ Futures process is a risk-neutral martingale
§ f(t)=EQ[LT(T1,T2)]
§ We use Laplace Transform and apply Affine
Transform Analysis (Duffie, Pan & Singleton, 2000)
Edith Mandel | Greenwich Street Advisors, LLC
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22. Conclusions
— Lines between Automated Market-Making,
Algorithmic Execution & Alpha Trading are blurry
— Most alpha strategies are highly dependent on
passive execution
— Liquidity providers cannot avoid holding inventory and
taking risk
— Optimal execution is reliant on order over-sizing and
risk-management
— Opportunities for agency-style execution are limited
— Rigorous quantitative framework is key
Edith Mandel | Greenwich Street Advisors, LLC
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