Valuing embedded guarantees
Options and guarantees in life and savings products are valued with stochastic scenarios that are consistent with market prices.
GRA · Actuarial and Quantitative Risk
Spatial financeWhere capital meets hazard, exposure and transition
Financial and risk engineering for actuarial and quantitative risk
Financial engineering values and structures instruments whose payoffs depend on risk. On this platform it covers valuation of guarantees and options in insurance contracts, asset-liability matching, longevity and catastrophe risk transfer and economic scenario generation.
01Register
Financial and risk engineering for actuarial and quantitative risk on the record.
Method recordSTEM method
- MethodFinancial and risk engineering
- StewardActuarial and Quantitative Risk
- Applied inActuarial and Quantitative Risk
- Data3 inputs
- Checks3 validation steps
- Canonical pageSTEM Commons
02Application
What financial and risk engineering does here.
Financial and risk engineering designs instruments, models and processes to measure, price and transfer risk. It applies quantitative methods to portfolios, insurance and risk-sharing arrangements. In insurance and catastrophe, methods and modelling and capital markets and investment, financial engineering enables physical and operational risks to be priced and transferred to capital markets. It informs the design of instruments that fund prevention and recovery. The canonical description is on the STEM Commons.
Economic scenario generators
Interest rate, equity and credit scenarios are generated for capital and valuation, with calibration targets and validation documented.
Risk transfer structures
Longevity swaps and catastrophe bonds are analysed for how they transfer risk, their basis risk and counterparty exposure.
03Geography
Activity and exposure in Japan and Korea.
Night lights, population density and flood water over Japan and Korea, from NASA GIBS. Each layer carries its own date.
The interactive map needs JavaScript; the layer list and sources are below.
Layers 3
Activity and exposure, for this page
About this layer
- Evidence
- Observed
- Source
- VIIRS Black Marble (VNP46A2) (NASA LAADS DAAC)
- Provider
- NASA LAADS DAAC
- Licence
- NASA open data
- Vintage
- daily; Satellite radiance, corrected for moonlight and atmosphere
- Newest at build
- 2026-10-12
- Resolution
- about 500 m grid
- Uncertainty
- Satellite night-time radiance for the date shown; lights are a proxy for electricity use and outages, not a measurement of supply or access.
- Reached through
- this site's data relay, from gibs.earthdata.nasa.gov
About this layer
- Evidence
- Estimated
- Source
- Gridded Population of the World v4.11 (NASA SEDAC (CIESIN, Columbia University))
- Provider
- NASA SEDAC (CIESIN, Columbia University)
- Licence
- CC BY 4.0
- Vintage
- null; Census-based estimate, static (2020)
- Resolution
- about 1 km grid
- Uncertainty
- Census-based estimate of people per square kilometre in 2020, shown as exposure context; not a count of people affected by any hazard.
- Reached through
- this site's data relay, from gibs.earthdata.nasa.gov
About this layer
- Evidence
- Observed (clouds leave gaps)
- Source
- VIIRS Global Flood Product (NASA LANCE)
- Provider
- NASA LANCE
- Licence
- NASA open data
- Vintage
- daily; Satellite detection; clouds leave gaps
- Newest at build
- 2026-10-14
- Resolution
- about 250 m grid
- Uncertainty
- Satellite detection; clouds leave gaps. Satellite or model raster as the provider publishes it. Clouds, swath gaps and retrieval error leave gaps and noise; values are indicators, not measurements at a place.
- Reached through
- this site's data relay, from gibs.earthdata.nasa.gov
About this layer
- Evidence
- Observed (persistent cloud still leaves gaps)
- Source
- VIIRS NOAA-20 Level 3, 8-day (NASA LANCE)
- Provider
- NASA LANCE
- Licence
- NASA open data
- Vintage
- 8-day; Satellite 8-day composite; persistent cloud still leaves gaps
- Newest at build
- 2026-09-14
- Resolution
- about 1 km grid
- Uncertainty
- Satellite skin temperature of the ground over the 8 days ending on the date shown, a heat exposure indicator; not air temperature, heat index or a heat warning.
- Reached through
- this site's data relay, from gibs.earthdata.nasa.gov
About this layer
- Evidence
- Estimated
- Source
- GPM IMERG (NASA GES DISC)
- Provider
- NASA GES DISC
- Licence
- NASA open data
- Vintage
- daily; Satellite estimate, near real time
- Newest at build
- 2026-10-12
- Resolution
- about 2 km grid
- Uncertainty
- Satellite estimate, near real time. Satellite or model raster as the provider publishes it. Clouds, swath gaps and retrieval error leave gaps and noise; values are indicators, not measurements at a place.
- Reached through
- this site's data relay, from gibs.earthdata.nasa.gov
About this layer
- Evidence
- Observed
- Source
- GHRSST MUR25 (NASA JPL PO.DAAC)
- Provider
- NASA JPL PO.DAAC
- Licence
- NASA open data
- Vintage
- daily; Satellite analysis
- Newest at build
- 2026-10-12
- Resolution
- about 2 km grid
- Uncertainty
- Satellite analysis of how far sea temperature departs from its usual value for the date shown; a marine heat indicator, not a coral bleaching alert.
- Reached through
- this site's data relay, from gibs.earthdata.nasa.gov
Keyboard, with the map focused
Hold Ctrl or ⌘ and scroll to zoom
Latest available
NASA GIBS / EOSDIS · ASTER GDEM (METI, NASA) · Blue Marble (NASA) · © OpenStreetMap contributors (ODbL) · Natural Earth
Loading the latest NASA imagery.
Drag to move. Ctrl or ⌘ and scroll, pinch or the buttons to zoom; hover for the values under the pointer; reset returns to the region.
Activity and exposure, framed on Japan and Korea.Satellite and model products as NASA publishes them, each with its own date. They are indicators, not assessments of any place.
Data: NASA GIBS · ASTER GDEM · Blue Marble · © OpenStreetMap contributors · Natural Earth · NASA EONET · U.S. Geological Survey · CIESIN/Columbia, NASA SEDAC HBASESources and licences
- We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS). Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS). Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- VIIRS Black Marble night-time lights, NASA Goddard Space Flight Center; distributed by the NASA Level-1 and Atmosphere Archive and Distribution System (LAADS DAAC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- Center for International Earth Science Information Network (CIESIN), Columbia University. 2018. Gridded Population of the World, Version 4 (GPWv4): Population Density, Revision 11. NASA Socioeconomic Data and Applications Center (SEDAC). Licensed under CC BY 4.0. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). doi:10.7927/H49C6VHW. CC BY 4.0
- VIIRS near-real-time products (flood, land surface temperature, snow cover, corrected reflectance), NASA LANCE; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- GPM IMERG precipitation, NASA Precipitation Processing System; distributed by the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- GHRSST Level 4 MUR analyses, NASA Jet Propulsion Laboratory; distributed by the NASA Physical Oceanography DAAC (PO.DAAC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- ASTER GDEM is a product of METI and NASA (ASTER Global Digital Elevation Model V003, NASA LP DAAC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). Cite as: NASA/METI/AIST/Japan Spacesystems and U.S./Japan ASTER Science Team (2019). ASTER Global Digital Elevation Model V003. doi:10.5067/ASTER/ASTGTM.003. NASA open data
- Made with Natural Earth. Free vector and raster map data @ naturalearthdata.com. Public domain
- © OpenStreetMap contributors (ODbL), via NASA GIBS (coastlines, boundaries, roads and place names). Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). ODbL
- Blue Marble, NASA Earth Observatory; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- Context on the globe and flat map: coastlines, boundaries, roads and place names from NASA GIBS reference layers (OpenStreetMap data, ODbL, © OpenStreetMap contributors); Blue Marble imagery as an optional base; 3D terrain and the elevation read-out from the ASTER GDEM elevation colour index (5 m to 200 m classes, exaggerated for legibility). Boundaries are drawn as published and imply no position on any territory.
- Live events: NASA Earth Observatory Natural Event Tracker (EONET); events are indicative and keep their original source links.
- Live: NASA EONET Events are indicative, not authority warnings.
- Live: U.S. Geological Survey Events are indicative, not authority warnings.
- Context: CIESIN/Columbia, NASA SEDAC HBASE. Center for International Earth Science Information Network (CIESIN), Columbia University, and NASA Socioeconomic Data and Applications Center (SEDAC): Global Human Built-up And Settlement Extent (HBASE) 2010; Seto, Guneralp and Hutyra 2012, Global Grid of Probabilities of Urban Expansion to 2030; Global Urban Heat Island (UHI) Data Set, 2013.
- NASA GIBS: We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS).
- Optional layers (5 sources in the layer list: live, forecast, observed and context) print their provider credit on the map and here when switched on; forecasts are model output and derived indices are estimates.
Layers and dates
- Night-time lights, daily: VIIRS Black Marble (VNP46A2), NASA LAADS DAAC · 12 Oct 2026
- Population density, 2020: Population: CIESIN, Columbia University, Gridded Population of the World v4.11 (2018), NASA SEDAC, CC BY 4.0 · static
- Flood water, 3-day composite: VIIRS Global Flood Product, NASA LANCE · 14 Oct 2026
- Land surface temperature, day, 8-day composite: VIIRS NOAA-20 Level 3, 8-day, NASA LANCE · 14 Sep 2026
- Precipitation rate, daily mean: GPM IMERG, NASA GES DISC · 12 Oct 2026
- Sea surface temperature anomaly: GHRSST MUR25, NASA JPL PO.DAAC · 12 Oct 2026
04Data
What the method consumes.
Datasets and records used by financial and risk engineering on this platform, with the role each plays and the label its values carry. Sources are listed in the source register.
| Data | Role | Label |
|---|---|---|
| Market prices | Calibration | OBSERVED |
| Contract terms | Payoff structures | DECLARED |
| Scenario sets | Valuation inputs | MODELLED |
05Loss model
Loss exceedance, average annual loss and probable maximum loss.
The loss a portfolio in the footprint can expect per year and at the 1 in 100 and 1 in 250 levels that insurers and lenders price, from the same three blocks every catastrophe model uses. Teaching model with stated illustrative values, not a prediction. The map on this page shows Japan and Korea; the model itself is not tied to a place.
Controls
- Typical annual hazard intensity (location)
- 1.00 intensity index
- Spread of extremes (scale)
- 0.80 intensity index
- Intensity at which half the value is lost
- 4.00 intensity index
- Dispersion of vulnerability
- 0.55
- Share of value in the hazard footprint
- 40%
- Protection standard (return period)
- 50 years
Readouts
- Average annual loss
- 0.51% of value
- Loss at 1 in 100 years
- 24.5% of value
- Loss at 1 in 250 years
- 28.4% of value
- Intensity at 1 in 100 years
- 4.68 intensity index
Numbers, methods and sources
| Return period (years) | Intensity (intensity index) | Loss (% of value) |
|---|---|---|
| 1 | 0.09 | 0.00 |
| 2 | 1.27 | 0.00 |
| 4 | 1.91 | 0.00 |
| 7 | 2.47 | 0.00 |
| 13 | 3.00 | 0.00 |
| 24 | 3.51 | 0.00 |
| 44 | 4.02 | 0.00 |
| 82 | 4.53 | 23.55 |
| 154 | 5.03 | 26.44 |
| 287 | 5.53 | 28.87 |
| 536 | 6.03 | 30.88 |
| 1,000 | 6.53 | 32.53 |
Methods
- Gumbel extreme-value hazard Gumbel (1958), Statistics of Extremes, Columbia University Press
- Lognormal fragility (vulnerability) FEMA (2003), HAZUS-MH Technical Manual
- Exceedance-probability curve and average annual loss Grossi and Kunreuther (2005), Catastrophe Modeling, Springer
- Levee effect Di Baldassarre and others (2013), Socio-hydrology, HESS 17
- Uncertainty fan (parameter Monte Carlo) Spiegelhalter, Pearson and Short (2011), Visualising uncertainty about the future, Science 333
- One-at-a-time sensitivity (tornado) Saltelli and others (2008), Global Sensitivity Analysis: The Primer, Wiley
Data
The model runs on the teaching values set by the controls. To calibrate it for a place, read it against these admitted layers and series, which this page’s map can draw:
- Rivers Natural Earth
- Urban extents Natural Earth
- Cities Natural Earth
- Earthquakes M4.5+, past week (USGS) U.S. Geological Survey · register usgs.earthquake.summary-feeds
- Rain rate, last half hour (IMERG) NASA GPM IMERG Early · register nasa.gibs.context-live-layers
- River discharge forecast, 30 days with range (GloFAS via Open-Meteo) Open-Meteo.com (CC BY 4.0), Copernicus GloFAS · register open-meteo.public-pages
- Built-up and settlement extent, 2010 (HBASE, Landsat) CIESIN/Columbia, NASA SEDAC HBASE · register sedac.context-urban-layers
Across the six pillars, led by Nexus Consortium
- Experiments Labs
- Built in Actuarial and Quantitative Risk in Foundry
- Tested at Actuarial and Quantitative Risk in Universe
- Codified in Finance, Insurance and the Economy in Standards
- Published in Actuarial and Quantitative Risk in Reports
- Taught in Faculty of Finance and Economics in Academy
06Validation
How results are checked.
Models are back-tested, benchmarked against alternatives and reviewed by independent validation functions. Stress tests probe behaviour beyond historical data.
| Check | How it is done |
|---|---|
| Market consistency | Scenarios reproduce calibration instrument prices |
| Scenario validation | Generators are tested for realistic behaviour |
| Convergence | Results are checked for stability as scenario counts increase |
Models calibrated to normal markets can underestimate tail losses and correlation shifts. Complex instruments may obscure where risk ultimately sits.
07Twin and cascade simulator
Trace a shock to the balance sheet.
Assembled from the Nexus Standards area profile Insurance and reinsurance: the shocks it names, the systems and sectors that carry the loss, the controls that dampen it and the data that observe it. Pick an initiating shock and step through the cascade to see which exposures it reaches and where losses could concentrate. The Map view places the run on an example geography with open data. Every weight is a stated assumption. An exercise, not a forecast, a valuation, a rating or investment advice. To model a place of your own choosing, open the full System Builder.
Hazards
- Tropical cyclone
- Earthquake
- Ice-jam flood
- Wildfire
- Storm surge (set off downstream)
- Intense rainfall (set off downstream)
- River flood (set off downstream)
- Flash flood (set off downstream)
- Dangerous surf (set off downstream)
- Widespread power outage (set off downstream)
- Mass displacement (set off downstream)
- Coastal flood (set off downstream)
- Aftershock sequence (set off downstream)
- Fault surface rupture (set off downstream)
- Soil liquefaction (set off downstream)
- Slope slide (set off downstream)
- Rockfall (set off downstream)
- Tsunami (set off downstream)
Systems and couplings
- Insurance and reinsurance
- Banking Coupling
- Development finance institutions Coupling
- Humanitarian and civil society Coupling
- Agriculture and land use Coupling
Controls
NS-0Constitution and principlesNS-3Risk record UNIs (grammar, legacy crosswalk, allocation authority)NS-9Contextual UNIs (deployments, instances, programme instances)NS-10Policies and clauses (machine-readable obligations: definition, binding, evaluation and enforcement)NS-11Verification and monitoring (evidence, attestations, zero-trust conformance observation)NS-14Conformance and crosswalk to external standardsNRS-F3Insurance, catastrophe risk and protection gapsNRS-H113Hazard family: Financial-system fragility (NHS-1 soc.financial-system)NRS-U17Universe platform profile: Insurance NexusNRS-H71Hazard family: Deep-time and cosmic catastrophes (NHS-1 planet.deep-time)NRS-H65Hazard family: Planetary boundary transgressions (NHS-1 planet.boundary)NRS-F8Parametric and index-based risk transfer
Observation
- OECD Data Explorer (incl. Creditor Reporting System, insurance and pension statistics) (listed for reference)
- Insurance statistics (listed for reference)
- USGS earthquake GeoJSON summary feeds (listed for reference)
- Direct economic loss attributed to disasters in relation to global gross domestic product (GDP)
- Direct economic loss attributed to disasters in relation to global gross domestic product
- (a) Number of commercial bank branches per 100,000 adults and (b) number of automated teller machines (ATMs) per 100,000 adults
Example geography
- Western Europe: 152 hexagonal cells
- Rain rate, last half hour (IMERG), NASA GIBS
- Night lights tonight, outages (VIIRS Day/Night Band), NASA GIBS
- Surface water through cloud, 30 m (OPERA DSWx-S1 radar), NASA GIBS
- Carbon monoxide, smoke transport (AIRS), NASA GIBS
08Connections
Topics that rely on this method.
09Exposure, loss and capital
What it means for exposure, loss and capital.
The exposure, loss, scenario and capital views a risk officer, supervisor or ministry of finance would ask for, with the frameworks they report against. Structures follow supervisory and actuarial practice. Values are illustrative: never prices, ratings or advice.
Exposure and loss at return periods
How losses from financial and risk engineering for actuarial and quantitative risk grow with severity, gross and net of reinsurance, against capital.
| Return period | Annual probability | Gross loss | Net loss | Net, capital = 100 |
|---|---|---|---|---|
| 1 in 10 | 0.10 | 14 | 10 | 10 |
| 1 in 50 | 0.02 | 33 | 21 | 21 |
| 1 in 100 | 0.01 | 46 | 27 | 27 |
| 1 in 250 | 0.004 | 68 | 39 | 39 |
| Average annual loss | 3.1 | 2.2 | 2.2 |
NGFS climate scenarios · Network for Greening the Financial SystemIFRS S2 Climate-related Disclosures · ISSBTCFD recommendations · Financial Stability Board TCFDPrinciples for the effective management of climate-related financial risks · Basel Committee on Banking Supervision
10Stewardship
Who maintains the method.
Actuarial and Quantitative Risk stewards financial and risk engineering for the Consortium and reviews how it is applied across platforms.
11Questions
Questions and answers.
What are the limits of financial and risk engineering in this field?
Models calibrated to normal markets can underestimate tail losses and correlation shifts. Complex instruments may obscure where risk ultimately sits.
How are results checked?
Models are back-tested, benchmarked against alternatives and reviewed by independent validation functions. Stress tests probe behaviour beyond historical data.
Are the values on this page real?
The data names, roles and checks are real descriptions of practice. The canvas shows a design of the method’s use, not a run; no result is reported here.
Where else is this method applied?
The canonical method page lists every platform that applies it.
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