Cornish-Fisher expansion for real estate value at risk

Abstract

Value at risk is a convenient and popular risk measurement tool. It represents the maximum potential loss on a specific portfolio of financial assets given a specific time horizon and a confidence interval. Principally value at risk is used in finance for risk management, financial reporting and capital requirement. In direct real estate, the calculation of this risk measurement is still rare even if it is now common to compute and disclose it in numerous other fields of finance. Indeed nowadays, financial institutions are facing the important task of estimating and controlling their exposure to market risk following a scope of new regulations such as Basel II, Basel III, NAIC or Solvency II. In this context, financial institutions use internal models for estimating their market risk. The purpose of this paper is to investigate the possibility to use Cornish-Fisher expansion to assess real estate value at risk. We show how Cornish-Fisher approximation can quickly give more accurate measurements than traditional methodologies. In addition, practitioners can find here a methodology to assess quickly value at risk without too many loss of relevancy due to normal hypothesis which is relaxed in our proposal.After a review of literature on value at risk and of the existing methodologies, the paper describes the Cornish-Fisher expansion, the assumptions required to apply it and how the expansion is used to compute value at risk. Then, we apply the proposed model to a UK dataset index and compare the results obtained with those obtained with Gaussian assumption.