Delta-Hedging and Value at Risk Using Generalized Extreme Value Distribution Implied in the KOSPI 200 Index Options
This study empirically investigates the usefulness of the generalized extreme value(GEV) distribution implied in the KOSPI 200 index options in terms of effectiveness for delta-hedging and value at risk(VaR) that is related to the two component of Bakshi and Madan(2000)'s option value equation, respectively. As benchmark models, we use Black and Scholes(1973) model(BS), two-lognormal mixture model(TLM) and Variance-Gamma model(VG). GJR-GARCH and normal distribution are used as time-series model of underlying asset returns. Because call option prices are not perfectly correlated with put option prices, the information contents of the call option price are different from those of put options market price. So, under the non-complete market and the limited arbitrage, we examine whether the information implied in call(put) option market price is more useful in the call(put) option market. We find that, in case of delta-hedging, although there is no model that dominate other models within all range of exercise prices, the implied parameter of GEV is the most stable among all the models and GEV is more useful during the recent comparative periods. Also, in the non-complete market, the performance of GEV is improved much more incrementally than those of the other models. Back-testing results of VaR show that, of all the models, GEV yields the least number of violation for the industry standard for 10 day VaR at high confidence levels of 99% but there is no model that dominate other models within all range of confidence levels like delta hedging. In the entire density forecast evaluation, GEV is not useful unlike the performance around the tail of the implied distribution.
Value at Risk
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