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Efficient Value at Risk - Risk Factor Mapping

Johansson Casserstål, Philip LU and Stenander Eklund, Oscar LU (2026) In Master's Theses in Mathematical Sciences FMSM01 20261
Mathematical Statistics
Abstract
This project examines whether a Taylor-based risk-factor mapping framework can
accurately and efficiently estimate Value at Risk for option-heavy portfolios without
the high computational cost of full revaluation. The method maps changes in portfolio
value to a selected set of market risk factors, including equity spot returns, foreign
exchange rates, interest-rate curves, and principal components of implied-volatility
surfaces. Portfolio sensitivities, including spot gamma, second-order volatility terms,
and spot-factor cross sensitivities, are calculated using bump-and-reprice finite
differences.
The framework is evaluated in two dimensions. Firstly, the Taylor approximation
is compared with full revaluation using historical... (More)
This project examines whether a Taylor-based risk-factor mapping framework can
accurately and efficiently estimate Value at Risk for option-heavy portfolios without
the high computational cost of full revaluation. The method maps changes in portfolio
value to a selected set of market risk factors, including equity spot returns, foreign
exchange rates, interest-rate curves, and principal components of implied-volatility
surfaces. Portfolio sensitivities, including spot gamma, second-order volatility terms,
and spot-factor cross sensitivities, are calculated using bump-and-reprice finite
differences.
The framework is evaluated in two dimensions. Firstly, the Taylor approximation
is compared with full revaluation using historical data from 2022 to 2026 and
randomized option-heavy portfolio tests. Secondly, several VaR scenario-generation
models are tested, including EWMA, GARCH, GJR-GARCH and state-dependent
extensions, in order to assess their ability to capture time-varying volatility, tail risk
and violation clustering. The VaR forecasts are evaluated using exceedance backtesting,
unconditional coverage tests and duration-based tests for violation independence.
The results show that the Taylor-based approach closely matches full-revaluation
estimates, with low average relative errors and similar exceedance patterns during
backtesting. Additional analysis of stock, foreign exchange, and bond instruments
indicates that the remaining approximation errors are mainly driven by option
nonlinearity. The best-performing VaR specifications produce violation rates close
to the expected levels and show no evidence of violation clustering. Overall, the
results suggest that the framework can significantly reduce scenario valuation cost
while preserving the main risk signals of full revaluation. (Less)
Please use this url to cite or link to this publication:
author
Johansson Casserstål, Philip LU and Stenander Eklund, Oscar LU
supervisor
organization
course
FMSM01 20261
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Value at Risk (VaR), Risk Factor Mapping, Filtered Historical Simulation (FHS), State-Dependent Sampling, GJR-GARCH, Taylor Approximation, Principal Component Analysis (PCA), Option Pricing, Bump and Reprice, VaR Backtesting
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMS-3569-2026
ISSN
1404-6342
other publication id
2026:E95
language
English
additional info
Omslag uppladdat av admin Susann Nordqvist
id
9243223
date added to LUP
2026-07-01 10:31:36
date last changed
2026-07-13 14:00:49
@misc{9243223,
  abstract     = {{This project examines whether a Taylor-based risk-factor mapping framework can
accurately and efficiently estimate Value at Risk for option-heavy portfolios without
the high computational cost of full revaluation. The method maps changes in portfolio
value to a selected set of market risk factors, including equity spot returns, foreign
exchange rates, interest-rate curves, and principal components of implied-volatility
surfaces. Portfolio sensitivities, including spot gamma, second-order volatility terms,
and spot-factor cross sensitivities, are calculated using bump-and-reprice finite
differences.
The framework is evaluated in two dimensions. Firstly, the Taylor approximation
is compared with full revaluation using historical data from 2022 to 2026 and
randomized option-heavy portfolio tests. Secondly, several VaR scenario-generation
models are tested, including EWMA, GARCH, GJR-GARCH and state-dependent
extensions, in order to assess their ability to capture time-varying volatility, tail risk
and violation clustering. The VaR forecasts are evaluated using exceedance backtesting,
unconditional coverage tests and duration-based tests for violation independence.
The results show that the Taylor-based approach closely matches full-revaluation
estimates, with low average relative errors and similar exceedance patterns during
backtesting. Additional analysis of stock, foreign exchange, and bond instruments
indicates that the remaining approximation errors are mainly driven by option
nonlinearity. The best-performing VaR specifications produce violation rates close
to the expected levels and show no evidence of violation clustering. Overall, the
results suggest that the framework can significantly reduce scenario valuation cost
while preserving the main risk signals of full revaluation.}},
  author       = {{Johansson Casserstål, Philip and Stenander Eklund, Oscar}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Efficient Value at Risk - Risk Factor Mapping}},
  year         = {{2026}},
}