Jumps in High Volatility Environments and Extreme Value Theory Abhinay Sawant March 4, 2009 Economics 201FS.

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Presentation transcript:

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: Assumption: t distribution is approximately normal for high sample size

Results: Financial Stocks Company Namez QP z TP Bank of America (BAC) Bank of New York (BK)– Citigroup (C) Capital One Financial (COF) Goldman Sachs (GS) JPMorgan Chase (JPM) Morgan Stanley (MS) Regions Financial Corp. (RF) U.S. Bancorp (USB) Wells Fargo (WFC)

Results: Non-Financial Stocks Company Namez QP z TP Cisco (CSCO) Intel (INTC) Hewlett-Packard (HPQ) Pfizer (PFE) Merck (MRK) Johnson & Johnson (JNJ) Wal-Mart (WMT) Procter & Gamble (PG) PepsiCo (PEP) Lockheed Martin (LMT) Caterpillar (CAT) Honeywell (HON)

Jumps in High Volatility Environments Regression of Realized Volatility on Z-Scores Comparisons across Industries

Extreme Value Theory

Extreme Value Theory: Background Theory General Pareto Distribution (GPD) describes values of x above the threshold u: ξ and β are to be estimated using Maximum Likelihood Estimation Hill’s Estimator:

Extreme Value Theory: Background Theory Extreme Value Theory allows for the estimation of risk metrics:

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?