Report

Jumps in High Volatility Environments and Extreme Value Theory Abhinay Sawant March 4, 2009 Economics 201FS Overview Jumps in High Volatility Last Environment: Updated method from previous time Extreme Value Theory: Read current literature on topic but haven’t decided how to apply it to data Set-Up of Test Pre-Lehman Period: All data through September 12, 2008 Post-Lehman Period: September 15, 2008 – January 4, 2009 (78 days) Difference of Sample Means t Test: t X 2 X1 s12 s22 n1 n2 Assumption: t distribution is approximately normal for high sample size Results: Financial Stocks Company Name zQP zTP Bank of America (BAC) 1.631 1.669 Bank of New York (BK) –0.483 -0.578 0.354 0.459 Capital One Financial (COF) -0.603 0.426 Goldman Sachs (GS) -0.633 -0.568 1.727 1.748 -0.255 -0.319 Regions Financial Corp. (RF) 1.650 1.653 U.S. Bancorp (USB) 0.055 0.048 Wells Fargo (WFC) 0.944 1.012 Citigroup (C) JPMorgan Chase (JPM) Morgan Stanley (MS) Results: Non-Financial Stocks Company Name zQP zTP Cisco (CSCO) -1.875 -1.797 Intel (INTC) -1.472 -1.476 Hewlett-Packard (HPQ) -1.547 -1.477 Pfizer (PFE) -0.053 0.015 Merck (MRK) -0.086 -0.065 Johnson & Johnson (JNJ) -0.161 -0.222 Wal-Mart (WMT) -2.193 -2.070 Procter & Gamble (PG) 0.734 0.865 PepsiCo (PEP) 0.051 0.096 Lockheed Martin (LMT) -0.860 -0.720 Caterpillar (CAT) -4.385 -4.246 Honeywell (HON) -2.991 -2.760 Jumps in High Volatility Environments Regression of Realized Volatility on Z-Scores Comparisons across Industries Extreme Value Theory Extreme Value Theory Extreme Value Theory: Background Theory General Pareto Distribution (GPD) describes values of x above the threshold u: F ( x | x u) 1 1 ( x u) 1 0 ξ and β are to be estimated using Maximum Likelihood Estimation Hill’s Estimator: 1 k 1 ln X i ,n ln X k ,n k 1 i 1 Extreme Value Theory: Background Theory Extreme Value Theory allows for the estimation of risk metrics: n VaRp u p 1 Nu VaRp ˆ u ES p 1 1 ˆ Extreme Value Theory: Current Literature High-frequency tail estimation has efficiency benefits since intraday data allows for observable extremes (Cotter and Longin, 2004) Margin setting based on closing prices alone underestimates the risk, when compared with intraday data (Cotter and Longin, 2004) High-frequency volatility estimator based on EVT provides superior forecasting abilities when compared to GARCH discrete time models (Bali and Weinbaum, 2006) Further Direction Does the financial crisis period offer extreme values of returns and can GPD model adequately estimate these values of returns? At high frequency, do the extreme intraday returns represent jumps or rapid movement in prices?