Index Options Market Research Articles

A Tractable Framework for Option Pricing with Dynamic Market Maker Inventory and Wealth

We develop a tractable dynamic model of an index option market maker with limited capital. We solve for the variance risk premium and option prices as a function of the asset dynamics and market maker option holdings and wealth. The market maker absorbs end users’ positive demand and requires a more negative variance risk premium when she incurs losses. We estimate the model using returns, options, and inventory and find that it performs well, especially during the financial crisis. The restrictions imposed by nested existing reduced-form stochastic-volatility models are strongly rejected in favor of the model with a market maker.

Lower Boundary Conditions and Pricing Efficiency Testing of Indian Index Options Market : Empirical Evidence from Nifty 50 Index

This article examined the pricing efficiency of the Nifty 50 index options market by empirically testing the lower boundary conditions (LBCs), a model - free approach. The study covered a period from April 1, 2012 to March 31, 2018. The violations of LBCs indicated that options were underpriced (mispriced). The frequency and magnitude of mispriced signals were examined according to liquidity and maturity of the options contracts. This was done with the view that mere mispricing of options does not indicate inefficiency of the market. It is the opportunity to extract abnormal profit (arbitrage) from these mispriced signals which poses a serious threat to the market efficiency. It was observed that most of the mispriced signals were concentrated at the thinly traded region and options which were going to get expired. The magnitude of mispriced signals at the thinly traded region and options which were going to get expired was significantly larger than the moderately and highly traded levels and options, which were far away from the maturity date. Furthermore, in order to validate whether the differences in the magnitude of violations were statistically significant, the hypotheses were formulated and tested for both the call and put options. The results of the study suggested that the Indian index options market during the period of study was efficient as most of the mispriced signals were not exploitable due to lack of liquidity.

Strategies for Improving V-KOSPI 200 Index

The study examines not only the methods for eliminating stale or abnormal prices but also strategies for enhancing liquidity in the KOSPI 200 index options market, for compensating the defects of V-KOSPI 200. First, introducing market making scheme in the KOSPI 200 options market can be the direct solution to prevent temporary fluctuations and spikes of the index arising from abnormal orders and to alleviate unnatural low variability (level) of the index through decreasing the use of stale market prices (model prices). Second, if weekly options underlying KOSPI 200 index are available for trading and investor interest in the weeklys are surged, Korea Exchange can enhance V-KOSPI 200 to include series of KOSPI 200 weekly options. The inclusion for at least 5~6 weekly options available for trading allow V-KOSPI 200 to be calculated with KOSPI 200 index option series that most precisely match the 30-day target time-frame for expected volatility that the Index is intended to represent. Along with these strategies for enhancing liquidity in the KOSPI 200 index options market, the study suggests the methodology which can prevents temporary fluctuations and spikes of the index by substituting stale or abnormal prices for normal prices.

Probability weighting functions obtained from Hong Kong index option market

In this paper we estimate the pricing kernel from the Hong Kong index option market and obtain the empirical probability weighting functions based on the rank-dependent expected utility. The empirical pricing kernel is estimated semi-parametrically as the ratio of the risk-neutral and objective densities. We employ a two-step estimation procedure to estimate the objective and risk-neutral densities under a consistent parametric framework of the non-affine generalised autoregressive conditional heteroskedasticity (G.A.R.C.H.) diffusion model. In the first step, we develop a continuous particle filters-based maximum likelihood estimation method to estimate the objective parameters of the G.A.R.C.H. diffusion model using the Hang Seng Index (H.S.I.) returns. In the second step of our estimation, we depart from the usual pure calibration approach and use the H.S.I. option prices to estimate the risk-neutral parameters of the G.A.R.C.H. diffusion model by constraining certain parameters to be consistent with the time-series behaviour of H.S.I. returns. Based on the estimated objective and risk-neutral parameters, the objective and risk-neutral densities are obtained by inverting the corresponding characteristic functions. Empirical results indicate that the empirical pricing kernel estimated from the Hong Kong index option market is non-monotonic and the estimated probability weighting functions are S-shaped, which implies that investors underweight small probability events and overweight large ones.

Index Option Anomalies: How Real Are They?

We examine empirical “puzzles” documented in several high profile studies of the market for S&P 500 index options, such as the overpricing of out-of-the money (OTM) put options and at-the-money (ATM) straddles. We find that without any exception the theoretical bases of these studies have ignored persistent features of the index option market data such as the wide bid-ask spreads for OTM options, the partial segmentation of the market for puts and calls, and the inconsistency of the parameter estimates for different maturity options, which we document in our data. We present simple theoretical models of the end user option trader that incorporate these features and are parsimonious in terms of other assumptions. We find that these puzzles disappear under such conditions and conclude that these apparent anomalies are probably due to the omission of the above features.

Variance and skew risk premiums for the volatility market: The VIX evidence

AbstractWe extract variance and skew risk premiums from volatility derivatives in a model‐free way and analyze their relationships along with volatility index and equity index returns. These risk premiums can be synthesized through option trading strategies. Using a time series of option prices on the VIX, we find that variance swap excess return can be partially explained by volatility index and equity index excess returns while these latter variables carry little information for the skew swap excess return. The results sharply contrast with those obtained for the equity index option market underlining very specific characteristics of the volatility derivative market.

Testing the Efficiency of Indian Index Options Market by Employing the Box - Spread Strategy : Empirical Evidence from S&P CNX Nifty Index

Testing the Efficiency of Indian Index Options Market by Employing the Box - Spread Strategy : Empirical Evidence from S&P CNX Nifty Index

Market Reform and Efficiency: The Case of KOSPI200 Options

ABSTRACTThe Korean government and exchange have identified a need to regulate excessive speculative trading and to protect domestic individual investors from foreign and professional traders. As such, they have proposed an options market reform that requires higher levels of margin accounts for options trading and that increases the basic options multipliers in the KOSPI200 options market. This study examines how this market reform affects the price disagreement and adjustment behaviors of the index options market. Our analyses indicate that the efficiency and information quality of out-of-the-money options trades have increased since the reform took effect.

Conic asset pricing and the costs of price fluctuations

Prudent upper and lower valuations from the literature on arbitrage free two price economies provide risk characteristics driving required returns. The risk characteristics assess the risk of price fluctuations. The difference between the upper and lower prudent valuations can be viewed as a capital charge. In addition the lower valuation assesses the down side tail risk. The required risk characteristics may be estimated on a daily basis from past data and we elaborate on how to perform such upper and lower valuations using distorted expectations. Details are provided for calculations using just the raw data, or by first fitting a probability distribution, or in terms of estimated arrival rates for jumps. The valuations are obtained with a dynamic calibration of a parametric distortion on the S&P 500 index options market. Results for required returns based on capital charges and down side risk compensation show an improvement when risk is represented by the arrival rates of jump sizes. For risk assessments based on arrival rates, capital charges constitute between 67 and 85% of the required return. The rest being a charge for downside risk exposures. After the introduction of risk characteristics into required returns there is little scope for covariation measures like asset betas. Different proposed constructions for required returns deliver differences in the value of an invested dollar and associated differences in asset rankings across time.

Call & Put Butterfly Spreads Test of SET50 Index Options Market Efficiency and SET50 Index Options Contract Adjustment

Call & Put Butterfly Spreads Test of SET50 Index Options Market Efficiency and SET50 Index Options Contract Adjustment

From funding liquidity to market liquidity: Evidence from the index options market

AbstractThis study examines the relationship between funding liquidity and market liquidity using daily data on the S&P 500 index options. We find that options market liquidity is positively correlated with funding liquidity after controlling for market uncertainty. Further analysis reveals that the positive relationship between funding liquidity and market liquidity in the options market is mainly driven by short‐term and deep out‐of‐the‐money options. Our results remain robust after controlling for the confounding effects of the equity market and different data frequencies.

An Empirical Study of the Cross Market Efficiency of the Index Options Market: A Case Study from the Italian Derivatives Market During and Post the Financial Crisis

This study examines the cross-market efficiency of the FTSE/MIB index options contracts traded on the Italian derivatives market (IDEM) between 1st October 2007 and 31st December 2012, a period including the financial crisis, using daily option prices. Two fundamental no-arbitrage conditions are tested: the lower boundary condition (LBC) and the put/call parity (PCP) condition while taking into account the role of transaction costs in mitigating the number of violations reported. Ex-post tests of LBC and PCP revealed a low incidence of mispricing in this market. Furthermore, to check the robustness of the results obtained by the ex-post tests, ex-ante tests were applied to PCP violations occurring within a one-day lag. The results showed a significant drop in the number of profitable arbitrage strategies. Overall, the number and monetary value of the violations reported declined during the post financial crisis period compared to those during the financial crisis period. The findings obtained from these tests generally support the cross-market efficiency of the Italian index options market during the sample period, though some violations were occasionally reported.

Determinants of Violations in the SET50 Index Options Pricing Relationships: Put-Call-Futures Parity and Box Spread Tests

Although SET50 Index Options, the only option product on Thailand Futures Exchange, has been traded since October 29, 2007, it has faced the liquidity problem. The SET50 Index Options market must offer a risk premium to compensate investors for liquidity risk. It may cause violations in options pricing relationships. This research therefore uses daily data from October 29, 2007 to December 30, 2016 to compare the violations in SET50 Index Options pricing relationships before and after change in contract specification on October 29, 2012 and investigate determinants of these violations using Tobit model. Two tests of SET50 Index Options pricing relationships, Put-Call-Futures Parity and Box Spread, are employed. The test results of Put-Call-Futures Parity show that the percentage and baht amount of violations in many cases are greater in the period before the modification of SET50 Index Options. Without transaction costs, we also see more Box Spread violations before contract adjustment. However, after taking transaction costs into account, there are more percentage and baht amount of Box Spread violations in the later time period. The estimation of Tobit model shows that the violation sizes of both Put-Call-Futures Parity and Box Spread, excluding transaction costs, depend on the liquidity of SET50 Index Options market measured by option moneyness and open interest. The SET50 Index Options contract specification, especially exercise price, also significantly affects the size of violations, though the direction of a relationship is not cleared.

A New Predictor of U.S. Real Economic Activity: The S&P 500 Option Implied Risk Aversion

We propose a new predictor of U.S. real economic activity (REA), namely the representative investor's implied relative risk aversion (IRRA) extracted from S&P 500 option prices. IRRA is forward-looking and hence, it is expected to be related to future economic conditions. We document that U.S. IRRA predicts U.S. REA both in- and out-of-sample once we control for well-known REA predictors and take into account their persistence. An increase (decrease) in IRRA predicts a decrease (increase) in REA. We extend the empirical analysis by extracting IRRA from the South Korea, UK, Japanese and German index option markets. We find that South Korea IRRA predicts the South Korea REA both in- and out-of-sample, as expected given the high liquidity of its index option market. We show that a parsimonious yet flexible production economy model calibrated to the U.S. economy can explain the documented negative relation between risk aversion and future economic growth.

옵션 거래 승수 인상에 따른 유동성 및 프리미엄의 변화

한국거래소에서 거래되는 KOSPI200 지수 옵션은 한때 거래량 기준으로 세계 1위 규모를 보이던 금융상품이었으나, 2012년 7월 만기 옵션 거래 승수가 1포인트당 10만 원에서 50만 원으로 상향되면서 거래가 큰 폭으로 위축되었다. 본 연구에서는 이러한 거래 승수 변화로 인해 옵션가격에 반영된 유동성 위험 프리미엄 효과가 실제로 변화하였는지 분석하였다. 실증 분석 결과 다음의 두 가지 결론을 도출하였다. 첫째, 옵션의 내재변동성과 EGARCH 모형으로 추정된 실현변동성의 차이로 정의된 변동성 스프레드의 움직임을 기존 문헌에 보고된 비유동성 변수가 유의하게 설명하는 것으로 나타나 옵션가격에 유동성위험 프리미엄 효과가 반영되어 있음을 확인하였다. 둘째, 변동성 스프레드는 거래 승수 인상 이후 콜옵션과 풋옵션 모두 감소하였으며, 특히 풋옵션에서 이러한 현상이 더욱 강하게 나타났다. 이는 옵션 거래 승수 인상 이후로 시장참여자가 옵션 매도를 할 유인이 줄어들었음을 의미해 매도에 따른 공급 감소와 매수자 중 개인투자자들의 시장진입이 어려워짐에 따라 매수에 의한 수요 감소의 개연성을 가지고 있다. 한편 위험관리 측면에서 헷지 목적으로 풋옵션을 매수하고자 하는 기존 시장참여자들 역시 원하는 시점에 풋옵션을 매수하기 어려워 정확한 헷지 전략을 구현하기가 어려워졌음을 시사한다.

The Information Flow of Option Markets during Global Financial Crisis: Where Do Informed Traders Trade?

Using the original transaction recodes from the Taiwan index options market, this paper is to investigate the trading behaviors of different investors and to capture the information flow between options market and stock market during global financial crisis. In contrast to previous studies, after controlling for the trading volume effects of different exercise prices with the same term-to-expiration, the empirical results show that market investors prefer to trade short-horizon contracts with larger trading liquidity and tend to choose the out-of- the-money options with higher leverage. In addition, there is a significantly reciprocal effect between options market and stock market. When the options trade increases, our findings are also consistent with the pooling equilibrium hypothesis. Particularly, the difference of trades between informed traders and individual investors during global financial crisis has responded to asymmetric information problems. Therefore, this paper concludes that the options trade of foreign institutional investors is more informative, and because of informative advantages, they are probably attracted to out-of-the money options.

20000000 200000 (Kospi200 Futures Price and Implied Volatility Smile of Kospi200 Options)

Korean Abstract: 코스피200 주가지수 선물과 코스피200 주가지수 옵션은 선물-풋-콜 패리티로 연결되어 있다. 본 연구는 비교적 장기간 선물 및 옵션의 거래 자료를 분석하여 선물의 가격이 행사가격별 옵션의 내재변동성에 차별적으로 미치는 영향을 분석하였다. 분석한 결과는 다음과 같다. 첫째, 선물가격이 고평가될수록 상대적으로 Call의 내재변동성은 상승하고 Put의 내재변동성은 하락하였고, 선물가격이 저평가될수록 상대적으로 Put의 내재변동성은 상승하고 Call의 내재변동성은 하락하였다. 이러한 선물의 영향력은 변동성이 낮은 경우에 더 높게 나타났다. 둘째, 선물가격의 영향력은 내가격옵션에서 더 크게 나타났다. 선물가격의 영향에 따라 옵션시장에서 변동성 스큐 모양과 변동성 스머크 모양이 나타났다. 셋째, 옵션의 잔존만기가 감소함에 따라 선물가격의 영향력이 증가하고 특히 내가격옵션의 내재변동성에 더 큰 영향을 주었다. 잔존만기가 감소함에 따라 변동성 스큐 현상과 변동성 스머크 현상이 심화되기도 하고 새로 발생하기도 하였다. 코스피200 주가지수 선물과 코스피200 주가지수 옵션시장처럼 동일한 기초자산을 갖는 파생상품의 가격은 서로 연결되어 있으며 영향을 준다는 사실을 가지고 옵션시장의 변동성 스마일 현상을 상당히 설명할 수 있었다. English Abstract: The KOSPI200 stock index futures and the KOSPI200 stock index options are linked to futures-put-call parity. This study analyzes the effect of the futures price on the implied volatility of option by exercise price by analyzing the long - term futures and options trading data. The results of the analysis are as follows. First, as the futures price is overvalued, the implied volatility of the call increases and the implied volatility of the put decreases, while the implied volatility of the put increases and the implied volatility of the call decreases as the futures price becomes undervalued. The influence of these futures is higher when the volatility is low. Second, the influence of futures prices is greater in ITM options. The volatility skew shape and the volatility smirk shape appeared in the option market depending on the influence of the futures price. Third, as the remaining maturity of the option decreases, the influence of futures price increases, especially the implied volatility of ITM options. As the remaining maturity decreases, the volatility skew and the volatility smirk shape become more severe and new. The fact that the prices of derivatives with the same underlying assets, like the KOSPI200 stock index futures and the KOSPI200 stock index options market, are linked and influenced, could explain the volatility smile of the option market considerably.

Skewness Versus Kurtosis: Implications for Pricing and Hedging Options

AbstractWe examine the relative influence of the skewness and kurtosis of option‐implied risk‐neutral density on pricing and hedging performance in the S&P 500 Index options market. We find that skewness exerts a greater impact on pricing and hedging errors than kurtosis. The model that considers skewness shows better performance for pricing and hedging options than the model that only considers kurtosis. Our results are consistent, even when the underlying return is extremely high or low, as well as for options on individual stocks. Overall, risk‐neutral skewness is more important than risk‐neutral kurtosis for pricing and hedging options.

Stratified Market Risk--An Analysis of Two Markets

This paper proposes a framework that decomposes the market risk into three components: upside, downside, and tail risk. Their risk premiums can be estimated using information from either the index options market or the stock market. The estimated premiums from both markets share two important properties: 1) The tail risk is highly priced; 2) Once the tail risk is excluded, the downside risk is barely priced. We also observe an important difference between the two markets: While the two sides of the market are priced highly asymmetrically in the index options market with all the equity premium attributed to the downside and none to the upside, the upside risk and downside risk both contribute significantly to explaining the cross-section of stock returns. Overall, our findings shed new light on the pricing of systemic risks and provide important evidence for market segmentation.

Higher moment risk premiums for the crude oil market: A downside and upside conditional decomposition

Relying on options written on the USO, an exchange traded fund tracking the daily price changes of the WTI light sweet crude oil, we extract variance and skew risk premiums in a model-free way. We further decompose these risk premiums into downside and upside conditional components and show that they can be partially explained by USO excess returns and, more importantly, these decomposed risk premiums enable a much better prediction of USO excess returns than the standard, or undecomposed, variance and skew risk premiums. A comparison with existing results for the equity index option market further confirms the usefulness of the decomposition for the crude oil market.