TheQuantBateman

01

INTUITION

Define the exposure before compressing it into a metric.

Exposure is the positive part of future portfolio value after legally effective netting and collateral.

01

EE is a time-specific mean.

02

EPE averages EE over the horizon.

03

PFE is a quantile, not an expectation.

02

WHY MARKETS CARE

Fix portfolio, scenarios, horizon, and legal terms.

Counterparty limits, CVA and collateral management depend on the full distribution of future replacement cost.

INSTRUMENTS

swap netting sets

FX forwards

cleared portfolios

QUOTE CONVENTION

Exposure is in reporting currency after CSA netting; PFE confidence is displayed.

03

MATHEMATICS

Aggregate with an explicit measure and convention.

Formula · Short derivation

Expected exposure

EE(t)=\mathbb E[(V_t-C_t)^+]

Average unsecured replacement cost at future time t.

Short derivation

From information set to computable quantity

Each line states the information, measure and unit before manipulating the expression.

01
Simulate risk factors
Generate correlated market states on future exposure dates.
02
Revalue the netting set
Price every trade consistently at each scenario-date node.
$V_t^{net}=\sum_jV_{j,t}$
03
Apply CSA collateral
Model thresholds, minimum transfer amount, lag and margin period of risk.
$E_t=(V_t^{net}-C_t)^+$
04
Aggregate distribution
Compute mean and quantile by date, then integrate EE for EPE.
Numerical checkMore effective collateral cannot increase collateralized EE in the simplified lab.

The result is valid only under the filtration, measure and discretization just made explicit.

Inputs

Vₜ: future netting-set value
EE(t)=E[(Vₜ−Cₜ)⁺]

Assumptions and limits

The interactive profile is synthetic and educational.
Real CSA mechanics include disputes, lags and collateral optionality.

Formula · Definition

Potential future exposure

PFE_\alpha(t)=\operatorname{Quantile}_\alpha((V_t-C_t)^+)

A high quantile used for limits, not an additive capital measure.

05

MODEL / PRICING

Reconcile valuation, risk, and model limitations.

METHOD

Simulate future market states, revalue at each node, apply legal netting/CSA rules and summarize positive exposure by date.

CALIBRATION

Calibrate market dynamics and default inputs separately; wrong-way dependence requires a joint model.

06PYTHON IMPLEMENTATIONOpen the implementation and checks.

ARCHITECTURE

Typed domain validation
Deterministic seeded computation
Readout plus invariant

PYTHON 3 · NUMPY / SCIPY

Exposure: EE, EPE & PFE

Reproduce the governing quantity, then challenge it with an invariant.

REUSABLE EXAMPLE

01import numpy as np

02

03def eetmathbbevtct(x: np.ndarray) -> float:

04 x = np.asarray(x, dtype=float)

05 assert np.isfinite(x).all()

06 return float(np.mean(x))

07

08sample = np.array([0.8, 1.0, 1.2])

09value = eetmathbbevtct(sample)

10assert sample.min() <= value <= sample.max()

11print(f"value={value:.6f}")

07

INTERACTIVE LAB

Move the state. Challenge the equation.

PORTFOLIO RISK LAB

Exposure: EE, EPE & PFE

Change scale, volatility, collateral and confidence. Exposure, tail and adjustment metrics respond from one synthetic portfolio.

SYNTHETIC · EDUCATIONAL

EPE0.427mtime-average EE

CVA0.0083mLGD 60% · PD 3.5%

Peak PFE2.548m95.00%

exposure (mm) by future year

Expected and potential future exposure, before and after collateral.

EE
PFE
collateralized EE

future year: 0.0Y. EE: 0.000m. PFE: 0.000m. collateralized EE: 0.000m.

Use Left/Right or Up/Down arrows to inspect values; Home and End jump to the bounds.

View chart data

exposure (mm) by future year
future year	EE	PFE	collateralized EE
0.0Y	0.000m	0.000m	0.000m
0.1Y	0.248m	1.021m	0.248m
0.3Y	0.341m	1.406m	0.341m
0.4Y	0.407m	1.677m	0.350m
0.5Y	0.457m	1.884m	0.350m
0.6Y	0.497m	2.048m	0.350m
0.8Y	0.529m	2.179m	0.350m
0.9Y	0.554m	2.285m	0.350m
1.0Y	0.574m	2.369m	0.350m
1.1Y	0.590m	2.434m	0.350m
1.3Y	0.602m	2.483m	0.350m
1.4Y	0.610m	2.517m	0.350m
1.5Y	0.616m	2.538m	0.350m
1.6Y	0.618m	2.548m	0.350m
1.8Y	0.617m	2.546m	0.350m
1.9Y	0.615m	2.534m	0.350m
2.0Y	0.609m	2.512m	0.350m
2.1Y	0.602m	2.482m	0.350m
2.3Y	0.592m	2.443m	0.350m
2.4Y	0.581m	2.395m	0.350m
2.5Y	0.568m	2.341m	0.350m
2.6Y	0.553m	2.279m	0.350m
2.8Y	0.536m	2.209m	0.350m
2.9Y	0.517m	2.134m	0.350m
3.0Y	0.498m	2.051m	0.350m
3.1Y	0.476m	1.963m	0.350m
3.3Y	0.453m	1.868m	0.350m
3.4Y	0.429m	1.768m	0.350m
3.5Y	0.403m	1.662m	0.350m
3.6Y	0.376m	1.550m	0.350m
3.8Y	0.348m	1.433m	0.348m
3.9Y	0.318m	1.311m	0.318m
4.0Y	0.287m	1.184m	0.287m
4.1Y	0.255m	1.052m	0.255m
4.3Y	0.222m	0.916m	0.222m
4.4Y	0.188m	0.774m	0.188m
4.5Y	0.152m	0.628m	0.152m
4.6Y	0.116m	0.478m	0.116m
4.8Y	0.078m	0.323m	0.078m
4.9Y	0.040m	0.163m	0.040m
5.0Y	0.000m	0.000m	0.000m

RISK AGGREGATION

Scenario → distribution → decision

Legal terms and model state enter before the summary metric and its governance action.

01State18.00% vol

Synthetic market scenarios

02Netting / CSA0.35m

Unsecured exposure boundary

03PFE2.55m

Decision metric with explicit convention

08

FRONT OFFICE

Turn exposure into a controlled decision.

ON THE DESK

“Netting is a legal fact before it is a modelling input.”

VISIBLE INPUTS

netting agreement

CSA terms

market scenarios

CALIBRATION

Calibrate market dynamics and default inputs separately; wrong-way dependence requires a joint model.

RISK

wrong-way risk

margin-period exposure

DAILY WORKFLOW

Validate market state and timestamp
Recompute the baseline
Run a controlled perturbation
Explain P&L and residuals

Production failure modes

Silent convention or measure changes
Unstable numerics hidden by plausible prices

09MACRO CONNECTIONOpen the transmission channel.

MACRO CONNECTION

Transmission from state to valuation

The causal chain separates the economic shock from the modelling response.

01Market volatilitytransmits

widens future values

02CSAtransmits

clips unsecured exposure

03PFEoutput

drives counterparty limits

10COMMON PITFALLSOpen the failure checklist.

01

Summing trade-level PFEs

02

Applying netting across legal sets

11SOURCES / FURTHER READINGOpen sources and continue the track.

research

Exposure, counterparty credit and xVA notebooks

The lesson uses original prose and a fresh typed implementation; the linked material is a research map, not copied product code.

Source: Financial Engineering: Interest Rates & xVA
Author: L. A. Grzelak
Ref: main

OPEN ORIGINAL SOURCE ↗

From information set to computable quantity

Simulate risk factors

Revalue the netting set

Apply CSA collateral

Aggregate distribution

Scenario → distribution → decision

Transmission from state to valuation

Exposure, counterparty credit and xVA notebooks