Discovery of Diverse and Realistic Financial Tail-Risk Using Generative Flow Networks

Adir Serruya; Gilad Katz

cs.LGOct 28, 2026

Discovery of Diverse and Realistic Financial Tail-Risk Using Generative Flow Networks

Authors: Adir Serruya, Gilad Katz

Organizations: Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Abstract

Accurate modeling of rare, high-impact financial events is essential for robust risk management. Sampling-based techniques such as Sequential Markov Chain Monte Carlo (SMCMC) generate diverse scenarios but inefficiently explore high-risk regions, while Deep Reinforcement Learning (DRL) converges on narrow sets of scenarios, limiting diversity. We present GRID, which uses Generative Flow Networks (GFlowNets) -- samplers that draw objects in proportion to a reward -- to systematically generate diverse and realistic financial tail-risk scenarios. Building on continuous GFlowNets, GRID introduces a flexible mixture-policy architecture with variable-specific distribution families for high-dimensional, sequential macro-financial data, together with plausibility constraints that keep generated trajectories realistic. A central practical advantage is robustness to reward-proxy imperfection: because GFlowNets sample proportionally rather than maximize, they remain broadly exploratory even when the oracle's out-of-sample accuracy is low -- an unavoidable reality in financial forecasting. On three real-world crises, GRID improves scenario diversity, realism, and tail-risk coverage over RL and MCMC baselines, and ablations over oracle architectures and distribution families yield practical insights into continuous GFlowNet behavior under noisy rewards.

Figures & tables

Fig. 1 : An overview of GRID. The method begins by modeling each environmental variable and the initial state, then explores the state space by sampling trajectories. Sampling is guided by the GFlowNet loss and feedback from the oracle.

Variable	Description
Volume_spx	Trading volume of the S&P 500 index
Close_ndx	Closing price of the NASDAQ-100 index
Volume_ndx	Trading volume of the NASDAQ-100 index
Close_vix	Closing value of the VIX (volatility index)
IRLTCT01USM156N	Long-term US interest rate
BAMLH0A3HYCEY	High-yield corporate bond spread

TABLE I : Initial macroeconomic environment variables defining the starting state

s_{0}

Fig. 2 : Learned action distribution for the Close_ndx variable at each of the 12 timesteps. The distribution shifts markedly across the horizon, showing that the time index enables GRID to learn time-dependent dynamics rather than applying a stationary policy.

Metric	Dot-Com (2002)	GFC (2008)	COVID-19 (2021)
$R^{2}\uparrow$	-0.4762	0.0942	-0.8638
RMSE $\downarrow$	11.59	4.2048	14.3532
MAE $\downarrow$	9.78	2.92	12.81

TABLE II : Oracle performance over a 24-month validation period. Lower MAE/RMSE is better; higher

R^{2}

is better. Low or negative

R^{2}

is typical in financial return prediction (see text).

GRID policy ( $\pi_{F},\pi_{B}$ )
Component / Setting	Value
Architecture	3-layer MLP, LeakyReLU, layer norm
Horizon $T$	12 timesteps
Replay buffer size	5000
Optimizer / learning rate	Adam / $5\times 10^{-4}$
Batch size	16

TABLE III : Key hyperparameters for GRID and the training-phase oracle. Baseline settings are given in Section VI-A .

Method	Median Reward			Q90 Reward
	2002	2008	2021	2002	2008	2021
GRID	43.11	31.13	18.12	58.57	54.52	100.00
REINFORCE	32.02	19.37	24.33	65.57	57.06	98.53
SAC	5.34	18.86	34.00	40.99	67.92	100.00
SMCMC	26.01	29.62	42.71	30.52	34.22	49.03

TABLE IV : Performance metrics (Median and Q90 reward) over 30 runs per algorithm on three crises. Higher is better; rewards clipped at 100.

Method	Traj Div (DTW)			Norm. Traj Div			Terminal-State Div			Norm. Terminal-State Div
	2002	2008	2021	2002	2008	2021	2002	2008	2021	2002	2008	2021
GRID	108.85	550.39	399.15	99.02	481.41	399.15	79.80	266.13	200.81	72.60	232.78	200.81
REINFORCE	94.31	402.24	229.17	90.71	352.80	229.17	77.24	271.92	160.71	74.29	238.50	160.71
SAC	260.25	136.10	264.38	244.84	136.10	264.38	182.53	92.27	187.60	171.72	92.27	187.60
SMCMC	182.01	186.48	164.81	163.69	167.92	139.29	100.93	103.47	96.53	90.77	93.17	81.58

TABLE V : Diversity metrics across three crises: raw and reward-normalized scores for full trajectories (DTW-based) and terminal states. Higher is better. Results from 100 trajectories per method.

Panel of Figure 8 — Fig. 3 : Reward distributions across 30 runs (6,000 trajectories per method) for the three crises. GRID produces a heavier high-reward tail and a broad spread, whereas SMCMC concentrates in a narrow band and the RL baselines place substantial mass on low rewards. The bimodality in 2021 ( 3(c) ) explains GRID’s lower median yet top Q90 there.

		2002 (Dot-Com)			2008 (GFC)			2021 (COVID-19)
Method	Top- $K$	Max	Mean	Std	Max	Mean	Std	Max	Mean	Std
GRID	10	0.374	0.267	0.073	0.433	0.247	0.132	0.500	0.420	0.059
GRID	50	0.380	0.265	0.084	0.562	0.276	0.133	0.533	0.430	0.067
REINFORCE	10	0.108	0.056	0.078	-0.534	-0.600	0.040	0.407	0.353	0.048
REINFORCE	50	0.136	0.066	0.054	-0.455	-0.559	0.045	0.425	0.374	0.035
SAC	10	-0.179	-0.243	0.044	0.416	0.374	0.024	-0.124	-0.143	0.013

TABLE VI : Trajectory similarity to actual crises: Pearson correlation between top-

K

risk-ranked trajectories and observed macroeconomic dynamics. Higher is better; bold marks the best mean per crisis and

K

. GRID attains the best or competitive mean realism with consistently high diversity (std comparable to or exceeding the RL baselines), while the RL baselines frequently produce anti-realistic (negatively correlated) trajectories.

	MaxDD (%)			VaR 95 (%)			CVaR 95 (%)
Method	2002	2008	2021	2002	2008	2021	2002	2008	2021
GRID	34.3	100	100	30.4	94.0	90.5	22.2	38.3	30.3
REINFORCE	0.0	9.6	10.7	0.0	0.0	7.5	0.0	0.0	0.0
SAC	32.8	65.2	33.0	27.5	56.9	25.3	12.9	45.7	12.8
SMCMC	24.3	19.7	4.9	15.6	2.3	0.0	8.0	0.0	0.0

TABLE VII : Tail-risk metrics. Higher values indicate discovery of more severe scenarios. GRID achieves the highest severity metrics while maintaining diverse coverage.

	2002		2008		2021
Oracle	$R_{\mu}$	N.DTW	$R_{\mu}$	N.DTW	$R_{\mu}$	N.DTW
Elastic Net	81.0	98.3	24.9	165.5	38.6	83.2
Ensemble	41.4	97.4	29.4	496.3	29.8	83.6
Gradient Boost.	12.0	113.2	5.5	194.5	6.2	216.2
MLP	27.1	90.8	80.2	189.7	77.7	149.0
Random Forest	4.9	118.4	13.9	176.6	10.5	158.2

TABLE VIII : Oracle-architecture ablation: GRID trained under five oracles. Reward mean (

R_{\mu}

) and reward-normalized DTW diversity (N.DTW) per crisis.

	2002		2008		2021
Family	$R_{\mu}$	N.DTW	$R_{\mu}$	N.DTW	$R_{\mu}$	N.DTW
Beta	35.7	137.7	100.0	181.0	100.0	328.2
Cauchy	22.2	81.4	15.0	106.1	30.4	153.4
Beta (Mix.)	35.4	171.8	76.4	128.1	99.3	410.3
Gaussian (Mix.)	34.5	139.6	75.0	134.7	49.3	48.4
Gaussian	29.4	213.3	56.0	98.9	26.3	61.1

TABLE IX : Distribution-family ablation: reward mean (

R_{\mu}

) and reward-normalized DTW diversity (N.DTW) per crisis. “Mix.” marks mixture families.

Crisis	Mixture	$\Delta$ Reward	$\Delta$ Eucl.	$\Delta$ DTW
2002	Beta	$-0.9\%$	$+23.3\%$	$+11.2\%$
2002	Gaussian	$+17.3\%$	$+22.8\%$	$+65.1\%$
2008	Beta	$-23.5\%$	$+3.9\%$	$+8.3\%$
2008	Gaussian	$+33.8\%$	$-7.7\%$	$+22.1\%$
2021	Beta	$-0.7\%$	$-5.5\%$	$-6.5\%$
2021	Gaussian	$+87.6\%$	$+485.1\%$	$+194.1\%$

TABLE X : Mixture effect: relative change (

\Delta\%

) of a mixture family over its corresponding single family (Gaussian mixture vs. Gaussian; Beta mixture vs. Beta), per crisis. Mixtures rescue weak families (large positive

\Delta

) while roughly preserving strong ones.

Method	Train (s)	Inference (ms/traj)
GRID	23.3	106.8
REINFORCE	3.9	27.7
SAC	7.2	6.6
SMCMC	–	51.8

TABLE XI : Computational cost on a commodity laptop CPU. Inference is per generated trajectory. SMCMC is non-trainable but must generate 2,000 trajectories per use case (effective cost

\approx

103.6 s).

Capability	GRID	SMCMC	DRL	Deep Gen.
Amortized one-shot sampling	✓	$\times$	✓	✓
High tail severity (MaxDD/VaR)	✓	$\times$	$\circ$	$\times$
Trajectory diversity	✓	✓	$\times$	$\circ$
Multi-modal coverage	✓	$\circ$	$\times$	$\times$
Robust to noisy oracle	✓	$\circ$	$\times$	–
Historical plausibility constraints	✓	$\times$	$\times$	$\times$

TABLE XII : Qualitative capability comparison, summarizing the trade-offs argued throughout and consistent with Tables IV , V , VI and VII . ✓: supported;

\circ

: partial;

\times

: not supported; –: not applicable.

Generative Flow Networks

Generative Flow Networks learn to sample diverse objects with probabilities proportional to their rewards.

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Deep generative models are increasingly used as simulators for downstream decision-making under data scarcity, but in risk-sensitive applications their usefulness depends on rare adverse scenarios rather than typical samples. Standard generative objectives prioritize bulk distributional fidelity, leaving low-probability tails vulnerable to localized optimization noise and making tail-dependent functionals unstable under finite simulation budgets. We introduce Diachronic Sample Integration (DSI), a test-time inference framework that ensembles generated samples across checkpoints from a stochastic training trajectory. DSI targets a checkpoint-mixture distribution that averages checkpoint-specific tail fluctuations rather than relying on a single brittle endpoint. We formalize this mechanism through a finite-budget bias-variance theory. Empirically, across multivariate synthetic processes and high-frequency trading data, DSI substantially reduces tail-estimation error compared to single-checkpoint baselines under fixed simulation budgets, outperforming standard diffusion and state-of-the-art tail-aware baselines without modifying the generative objective.

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