Cornish-Fisher Expansion for Commercial Real Estate Value at Risk
Bibliographic record
Abstract
The computation of Value at Risk has traditionally been a troublesome issue in commercial real estate. Difficulties mainly arise from the lack of appropriate data, the non-normality of returns, and the inapplicability of many of the traditional methodologies. As a result, calculation of this risk measure has rarely been done in the real estate field. However, following a spate of new regulations such as Basel II, Basel III, NAIC and Solvency II, financial institutions have increasingly been required to estimate and control their exposure to market risk. As a result, financial institutions now commonly use internal Value at Risk (VaR) models in order to assess their market risk exposure. The purpose of this paper is to estimate distribution functions of real estate VaR while taking into account non-normality in the distribution of returns. This is accomplished by the combination of the Cornish-Fisher expansion expansion with a certain rearrangement procedure. We demonstrate that this combination allows superior estimation, and thus a better VaR estimate, than has previously been obtainable. We also show how the use of a rearrangement procedure solves well-known issues arising from the monotonicity assumption required for the Cornish-Fisher expansion to be applicable, a difficulty which has previously limited the useful of this expansion technique. Thus, practitioners can find a methodology here to quickly assess Value at Risk without suffering loss of relevancy due to any non-normality in their actual return distribution. The originality of this paper lies in our particular combination of Cornish-Fisher expansions and the rearrangement procedure.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.011 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".