Taking fixed income, three levels of machine learning are applied to 1) identify jumps in time series; 2) cluster the jumps; and 3) propagate the jumps in the simulation. A key finding is that the common assumption of an underlying diffusion can be discarded. Presented at RiskMinds, Boston MA, September 24th 2018.

1. Solving BCBS-185 with Machine Learning
Dr. Peter Zeitsch
Boston, September 24th 2018

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Motivation
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Motivation (cont’d)
FB
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Motivation (cont’d)
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TSLA

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Agenda
 Review BCBS-185
– Salient points
– Implications  Black Swans
 Machine Learning
– Jump identification
– Clustering
– Jump simulation
 Re-assess the classical models
 Key Take-aways
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Preprint – submitted to Physica A
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BCBS - 185
 Guidelines released in 2010
– Applicable to all IMM banks
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BCBS-185 (cont’d)
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Counterparty Credit
 EPE calculations have several sub-models:
– Pricing functions
– Simulation model
 Risk Factor evolution through time (stochastic processes)
 Collateralization model
 Netting & Aggregating
 Collateral, Netting and pricing are well understood. This leaves the risk
factor model itself as the area for scrutiny
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The Methodology
 “forecasts against realized values”, “definition and calibration of the
stochastic processes”  need to model the fat tails.
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Methodology (cont’d)
 Merton 74
 Asset returns can be modelled as:
random walk + jump process
 Random walk is a “Brownian motion” or “log-normal”
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Methodology (cont’d)
 The random walk implies that the log-returns are Normally distributed.
 The addition of the jump process indicates that some of the log-returns
are not Normally distributed.
 Need to split them  Machine Learning
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ML I: Find the jumps
 Take the USD 5Y swap rate
 Filter the log-returns and classify them as either log-normal or jumps
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ML I: Find the jumps (cont’d)
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ML I: Find the jumps (cont’d)
 Did we find the log-normal component?
 QQ-plot indicates close agreement between the log-returns and a Normal
distribution as desired.
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ML II: Cluster Identification
 Back to the swap rate
 Volatility displays regime switching
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ML III: Simulation
 Propagate the clusters into the simulation
 Replicate the regime switching
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Back test the jump model
 Does the model agree with the price action in the market?
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The tails are
captured

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History of the Models
 Short rate modelling has concentrated on the continuous
component/Brownian motion
– Merton 72 (log-normal), Merton 74 (log-normal + jump), Vasicek 77 (mean reversion),
Cox-Ingersoll-Ross 85 (square root process), Hull-White 90 (extends Vasicek), Black-
Derman-Toy 90, Black-Karasinski 91, Longstaff-Schwartz 92 (multi-factor), Chen 96
(stochastic mean & vol)
– Heath-Jarrow-Morton 96 (full description of the curve e.g. Brace-Gatarek-Musiela)
 Limited interest in jump modelling
 Are there any other market dynamics that don’t agree with the Brownian
motion assumption?
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Fed Funds
 Policy rate set by the Federal Reserve
 Moves when the fed “hikes or cuts rates”
 What does the Machine Learning show?
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Fed Funds (cont’d)
 No log-normal/continuous component  purely jumps
 Again, clustering captures regime shifting
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Fed Funds (cont’d)
 Back testing shows good agreement
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Fed Funds (cont’d)
 Simulation replicates the price action
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Negative Rates
 JPY OIS: no Brownian motion but negative yield is modelled
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Summary
 Applications:
– Default modelling
– MBS, ABS  pre-payment risk
 3 key points:
– New approach to satisfying BCBS-185
– Technique employs machine learning to calibrate the model and propagate
the simulations
– Leads to a departure from classical modelling techniques
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