VaR and Expected Shortfall Based on Put Option Formula and Tail Volatilities & Correlations: 'The Need for New Valuation, Risk and Policy Making Models'

17 Pages Posted: 19 Jul 2015 Last revised: 21 Feb 2017

Date Written: July 17, 2015

Abstract

This paper presents an alternative method to calculate analytical VaR and Expected Shortfall – ES – using the Black & Scholes put option formula, Markowitz diversification concept of the covariance-variance matrix and tail price return histograms to calculate volatilities and correlations at the 1 and 5 percentile. The methodology based on option valuation suggests using exchange traded options to calculate VaR and ES parameters – it shares the same methodological framework with volatility dependent derivatives. The term “unwind in day-t” will be clarified by the definition of VaR to LIQUIDATION. The proposed VaR and ES methodologies allow computing risk metrics under different scenarios to anticipate what action to take in case there is a change in market behavior towards, say, systemic risk and a free fall of asset prices. The risk manager can chose between using data from a (i) calm market, (ii) falling market, (iii) market dominated by systemic risk, etc. – whichever the risk management committee feels best represents the near future. Economists and company analysts should be part of the risk management committee, because through their research they may suggest short term price forecasts not yet priced by the market, which can lead to dispensing with the EMH in the short run.

Keywords: VaR, CVaR, Black&Scholes, Markowitz, EMH, tail distribution parameters

JEL Classification: D81, D89, C13, D49

Suggested Citation

Crousillat, Cesar, VaR and Expected Shortfall Based on Put Option Formula and Tail Volatilities & Correlations: 'The Need for New Valuation, Risk and Policy Making Models' (July 17, 2015). Available at SSRN: https://ssrn.com/abstract=2632419 or http://dx.doi.org/10.2139/ssrn.2632419

Cesar Crousillat (Contact Author)

Universidad del Pacifico ( email )

Av. Salaverry 2020
Jesus Maria
Lima, Lima 18
Peru
0115112210099 (Phone)

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