Determinants of Put-Call Disparity: Kospi 200 Index Options

Abstract

Many studies find that traditional option pricing models fail to work in practice. The implied volatility smile is one example. In this study, we examine deviations of spot prices from prices implied by put-call parity for Korean KOSPI 200 index options, one of the most actively traded derivative products in the world. Deviations are significant and economically meaningful across different moneyness categories spanning deep-in-the-money to deep-out-of-the-money options. Determinants of put-call disparities for the KOSPI 200 index options include past spot return moments, cognitive biases, and prior option trading volume relative to spot trading volume. We show mispricing is more likely to occur after periods of extreme downturns in the stock market, implying demand for put options increases relative to call options when investors become more likely to insure against extreme loss. We also show that put-call disparity rates have predictive power for future spot returns due to overreaction of KOSPI 200 index option traders, rather than to information contained in option prices.

Keywords:

• Arbitrage
• Cognitive bias
• KOSPI 200 index options
• Put-call parity
• Volatility smile

Notes

1 World Federation of Exchanges IOMA 2018 Derivatives Report.

2 Our model assumes borrowers and lenders alike utilize the 91-day interest rate. In reality, borrowing and lending rates (to short stock) are different, both in terms of calculating put-call parity and across various market participants. However, the simplification is unlikely to materially affect the put-call parity calculations. We thank an anonymous referee for offering these explanations.

3 The use of percentage range deviations of the exercise price relative to the spot price to distinguish moneyness categories is common in the option literature (e.g., Rubinstein, 1985, Bakshi et al., 2000, Miao et al., 2018). We ran robustness tests using wider moneyness spreads, and the results of those tests show no material differences from the ones presented in our paper.

4 KOSPI Factsheet, 2012.

5 For much of our sample, retail investors dominated trading in KOSPI futures and options, accounting for well over 50% of KOSPI 200 options trading (Wall Street Journal, Korea Curbs Derivatives Markets, March 25, 2004). Ahn et al. (2008) make similar comments, arguing that the KOSPI options market offers a unique research opportunity in which the majority of active market participants are individual investors. The authors contend informed traders in KOSPI options can extract trading profits using their superior information-processing skills and/or their superior trading skills.

6 KOSPI 200 ETFs exist. For example, BlackRock offers the iShares Core KOSPI 200 ETF, which is intended to track the investment performance of the KOSPI 200.

7 The multiplier increased from 100,000 to 500,000 September 2012, and later reduced to 250,000 in March 2017. We use the current multiplier and exchange rate merely to provide a USD arbitrage reference point. The multiplier averaged 238,000 over our sample period, so the use of the current 250,000 multiplier serves as a reasonable reference point. The average disparity rate did not change much over the different multiplier regimes as illustrated in Figure 1.

8 We note that the options market closes 15 minutes after the spot market throughout our sample, posing possible synchronicity problems for our tests. To address this issue, we obtained intraday options day for the 6-year period 2004 – 2009. We matched the option data to the close of the spot market for each day. We repeat all tests reported in our paper on the 6-year period over the synchronized and non-synchronized data. The correlation between the disparity values for synchronized versus non-synchronized data equals 0.85, and the mean difference was very small (0.00004). We find no substantive differences in the magnitudes or p-values for slope estimates in our regression tests run on the synchronized and non-synchronized data during the 6-year period. These robustness tests offer evidence lessening concerns about synchronicity issues in our paper.

9 The GMM estimation method is preferred to the maximum likelihood estimation (MLE) method. As pointed out by Hall (2015), MLE methods require the imposition of an assumption about the distribution of the data. If the assumed distribution is incorrect, then the MLE method loses its optimal properties and resulting estimates may be inconsistent. Therefore, tests based on MLE estimation become joint tests of the economic model being examined and distributional assumptions imposed by the researcher. In contrast, the GMM method provides a way to estimate parameters and test whether the model “is consistent with the data based purely on moment conditions deduced from the economic model itself” (Hall, 2015, page 4).

10 Kim (2019) finds that past distribution moments are significant determinants of the volatility spread for the KOSPI 200 index and that the volatility spread is negatively related to subsequent KOSPI 200 index returns.

11 We re-ran the regression with the dummy variable equal to one when the disparity rate is negative, zero otherwise. The SD coefficient (representing the standard deviation effect when DISP is positive) is positive and significant at the 1% level in this regression.

12 Skewness has been shown to be a significant determinant of the cross-section of stock returns. Harvey and Siddique (2000) develop an asset pricing model where skewness is priced.

13 Individual investors in Korea are not permitted to short stocks in the KOSPI 200 index. Institutions and foreign investors are permitted to short sell stocks in the KOSPI. Due to the COVID-19 epidemic, in March 2020, the South Korean government imposed a short-selling ban on KSX listed stocks. In August 2020, the ban was extended another 18 months.

14 We also re-ran the regression after replacing DISP with the implied volatility spread (IV for call options minus IV for put options). When aggregating over all observations (i.e., the ALL column in our tables), the slope coefficient is significantly negative at the 0.10 level. The inclusion of the IV variable is particularly appropriate because increases (decreases) in IV indicate buying (selling) power. Our findings offer further support for our conclusion that the demand for calls increases relative to puts just prior to a downturn in market returns. We thank an anonymous referee for offering this suggestion.

15 We note that our negative coefficient on Ovol/Svol is consistent with Johnson and So (2012), who argue the negative relation is due to short sale constraints on stocks. According to Johnson and So (2012) “short sale costs lead informed agents to trade options more frequently for negative signals than positive ones, thus predicting a negative relation between relative option volume and future equity value.” [p. 263]