The research atlas · five chapters
Follow the risk.
Understand the decision.
Start with the question you would ask as an analyst. Each of these thirteen investigations explains the idea, shows what the experiment actually found, and tells you where the conclusion stops.
13 investigations · Questions, methods, and limitations
Market & Tail Risk
What could we lose, together?
Measure everyday losses, explore extremes, and test the connections that diversification depends on.
Measuring portfolio risk
How much could a portfolio lose on a bad day?
What we found In the saved 10,000-observation synthetic check, 95% daily VaR is 1.64% and ES is 2.07%. The losses beyond the threshold are more severe than the threshold itself.
Simulating uncertainty
How stable is a risk estimate across possible futures?
What we found The saved 100,000-path call estimate is 9.388, versus an analytical price of 9.413. The analytical value lies inside the simulated 95% interval, 9.300–9.475, for this one-year option.
Volatility is not constant
What changes when volatility remembers the past?
What we found The saved fit on 1,500 training observations produces a daily volatility forecast of 1.001%. This is a numerical forecast check; it does not establish superiority over constant volatility on future data.
Learning from the tail
What can the most extreme observations tell us?
What we found For the saved Pareto sample, estimated 99% VaR is 4.737 versus analytical 4.642; estimated ES is 7.319 versus 6.962. The fitted tail shape is 0.352 against a generating value of one third.
When diversification fails
Do assets become more dependent when it matters most?
What we found The saved 5,000-sample check estimates correlation 0.592 from a generating value of 0.600. Separate tests verify differences in tail dependence and portfolio VaR across copula families; correlation recovery alone does not validate crisis behavior.
Credit & Contagion
Whose failure becomes our loss?
Follow risk from a borrower's probability of default to trading counterparties and interconnected institutions.
Beyond the credit score
Can a default prediction be accurate and well calibrated?
What we found On 1,000 held-out synthetic applications, logistic regression records AUC 0.882, versus 0.861 for boosting. Extra complexity does not improve this ranking comparison.
Price the counterparty
What happens when exposure and default move together?
What we found The saved five-year flat-exposure check gives CVA 5.289 on exposure 100, with hazard 2%, recovery 40%, and discount rate 3%. This controlled example makes each ingredient inspectable.
Risk travels through networks
Can a financial network amplify an initial default?
What we found The graph convolution model has a higher Brier score than the one-round structural baseline in all three held-out seeds. Lower is better: the simpler mechanism-aware baseline wins this saved comparison.
Stress & Climate
What if the world changes?
Translate explicit economic and climate assumptions into conditional losses across different horizons.
Make the adverse case
Which combination of shocks would break the portfolio?
What we found The saved linear example reaches a 10% loss with an equity shock of −10% and a spread-factor shock of +5%, satisfying its constraint to numerical precision. The result is conditional on this transmission model.
A longer risk horizon
How do transition assumptions reshape portfolio losses?
What we found The saved demonstration contains six constructed pathways with 16 annual points each. Its delayed-transition carbon price reaches about 399 in 2050, compared with about 248 for net zero. These are generated scenario values, not official NGFS observations.
Model Reliability
Does the forecast keep its promise?
Assess uncertainty around a prediction, especially when yesterday's calibration stops describing today.
Hedging & Allocation
Which response earns its complexity?
Compare the costs and tail losses of learned decisions with simple strategies on equal terms.
Does learned hedging help?
Can a learned hedge improve the cost–risk tradeoff?
What we found Across all three saved held-out seeds, the neural hedge has higher 95% ES than delta hedging. Both reduce tail loss substantially relative to no hedge. The learned model has not earned its complexity in this benchmark.
Learning to allocate risk
Does an adaptive policy justify its additional complexity?
What we found The saved PPO policy has higher daily 95% ES than inverse-volatility allocation in all three held-out seeds. This fixed-budget synthetic benchmark supports the simpler baseline for that metric.