Two New Risk Metrics: Liquidity Asian Put VaR(TM) and Shortfall(TM) to LIQUIDATION Based on Tail Volatilities & Correlations 'The Need for New Valuation, Risk and Policy Making Models'

Abstract

This paper derives two new improved risk metrics LAPVaR and LAPSF. Traditional VaRDeltaNormal valuation exaggerates market and liquidity risks to the point it could be larger than the actual portfolio value. Put VaR – PVaR – as well as Put Shortfall – PSF – uses option theory to solve the problem that, under any circumstance, the risk amount is never greater than the portfolio value. Risk to LIQUIDATION means every day-t, a portion of portfolio assets-i, for integer i ϵ (1, N) is unwound without disturbing the market; thus the final unwind price equals the sum-product of asset-i and price-return-(i,t), where for each asset-i ϵ (1, N), there is t ϵ (1, Hi,t), such that day-Hi, t is the last unwind day of asset-i. This method calculates Asian PVaR – APVaR – and Asian PSF – APSF – because it’s marked at the asset-i average unwind price from day-1 to day Hi,t. A formula is derived to estimate a horizon-Ĥ necessary to measure analytic VaRs. Liquidity haircut-Li are incorporated endogenously modifying forward-i value in the analytic formulas – LAPVaR and LAPSF – representing a great advantage over calculating exogenously Liquidity Haircuts in traditional VaRHistorical and analytic VaRDeltaNormal. The new formula is compared to the traditional risk measure, the Bullet Historical VaR to LIQUIDATION – i.e. VaR Historical.

Keywords: LAPVaR, LAPSF, AVaR, ASF, VaR, SF, Market Risk, Liquidity Risk

JEL Classification: D81, D89, C13, D49