코스피200 지수옵션 델타의 이상치 분석

Abstract

This paper is an empirical study on delta violations of the KOSPI 200 index options to test the theoretical constraint established by Bergman et al.(1996), that is  ≤  C ≤ 1 and   ≤  P ≤  where  C and  P are deltas of call and put options respectively. I used daily price data of the near-maturity contracts from January 4, 2010 to June 9, 2016 to compute deltas. The delta violation is defined as follows; Type 1 violation is  C ≤  for call option or  P ≥  for put option, which means reverse reaction of option price to index change, and Type 2 violation is  C ≥  for call option or  P ≤  for put option, which means overreaction of option price. The most important finding of this paper is that the frequency and the size of delta violations are unexpectedly large. The relative frequencies of Type 1 (reverse response) and Type 2 (overreaction) violations are respectively 25.70% and 18.98% of call option deltas. Those of put option deltas are 22.68% and 17.83%. The average of delta of Type 1 is –1.2503 and that of Type 2 is 3.5465 for call options, and those for put options are 1.1681 and –3.5684. These statistics show that more than 40% of option deltas are violated from theoretical constraints and the average of violations are much larger than expected. These results suggest that KOSPI200 index options cannot be regarded as redundant assets and used as hedging devices. The frequency and size of violations give statistical evidence supporting popular conception that index options are gambles or speculative assets. Frequencies of violations appear to be related to moneyness, days to maturity and daily transaction volumes. Two of notable results among many findings in this paper are; the frequencies of Type 2 violations for deep in-the-money options are close to 50% regardless of option type, and the averages of Type 2 violations both for call and put options are much larger only when we have 11 to 15 days to maturity.