Implied Volatility of the KOSPI 200 Index Option Market

2015 ◽  
Vol 23 (4) ◽  
pp. 517-541
Author(s):  
Dam Cho
Keyword(s):  
Financial Crisis ◽  
Trading Volume ◽  
Implied Volatility ◽  
Spot Price ◽  
Strike Price ◽  
Market Pricing ◽  
Put Options ◽  
The Difference ◽  
Index Option ◽  
Option Market

This paper analyzes implied volatilities (IVs), which are computed from trading records of the KOSPI 200 index option market from January 2005 to December 2014, to examine major characteristics of the market pricing behavior. The data includes only daily closing prices of option transactions for which the daily trading volume is larger than 300 contracts. The IV is computed using the Black-Scholes option pricing model. The empirical findings are as follows; Firstly, daily averages of IVs have shown very similar behavior to historical volatilities computed from 60-day returns of the KOSPI 200 index. The correlation coefficient of IV of the ATM call options to historical volatility is 0.8679 and that of the ATM put options is 0.8479. Secondly, when moneyness, which is measured by the ratio of the strike price to the spot price, is very large or very small, IVs of call and put options decrease days to maturity gets longer. This is partial evidence of the jump risk inherent in the stochastic process of the spot price. Thirdly, the moneyness pattern showed heavily skewed shapes of volatility smiles, which was more apparent during the global financial crises period from 2007 to 2009. Behavioral reasons can explain the volatility smiles. When the moneyness is very small, the deep OTM puts are priced relatively higher due to investors’ crash phobia and the deep ITM calls are valued higher due to investors’ overconfidence and confirmation biases. When the moneyness is very large, the deep OTM calls are priced higher due to investors’ hike expectation and the deep ITM puts are valued higher due to overconfidence and confirmation biases. Fourthly, for almost all moneyness classes and for all sub-periods, the IVs of puts are larger than the IVs of calls. Also, the differences of IVs of deep OTM put ranges minus IVs of deep OTM calls, which is known to be a measure of crash phobia or hike expectation, shows consistent positive values for all sub-periods. The difference in the financial crisis period is much bigger than in other periods. This suggests that option traders had a stronger crash phobia in the financial crisis.

An Empirical Study on Implied Volatility Skew Using PCA

2016 ◽  
Vol 24 (3) ◽  
pp. 365-397
Author(s):  
Jin Woo Kim ◽  
Joon H. Rhee
Keyword(s):  
Financial Crisis ◽  
Implied Volatility ◽  
Structural Changes ◽  
Explanatory Power ◽  
Asset Price ◽  
Option Price ◽  
Principal Component ◽  
Underlying Asset ◽  
Put Options ◽  
Two Factors

This paper extracts the factors determining the implied volatility skew movements of KOSPI200 index options by applying PCA (Principal Component Analysis). In particular, we analyze the movement of skew depending on the changes of the underlying asset price. As a result, it turned out that two factors can explain 94.6%~99.8% of the whole movement of implied volatility. The factor1 could be interpreted as ‘parallel shift’, and factor2 as the movement of ‘tilt or slope’. We also find some significant structural changes in the movement of skew after the Financial Crisis. The explanatory power of factor1 becomes more important on the movement of skew in both call and put options after the financial crisis. On the other hand, the influences of the factor2 is less. In general, after financial crisis, the volatility skew has the strong tendency to move in parallel. This implies that the changes in the option price or implied volatility due to the some shocks becomes more independent of the strike prices.

Do the Option Prices Forecast Spot Price? Evidence from the KOSPI 200 Index Option Market

2011 ◽  
Vol 19 (3) ◽  
pp. 251-280
Author(s):  
Byungwook Choi
Keyword(s):  
Implied Volatility ◽  
Parametric Method ◽  
Trading Strategy ◽  
Stock Index ◽  
Rate Of Return ◽  
Spot Price ◽  
Option Prices ◽  
Daily Rate ◽  
Risk Neutral ◽  
Index Option

This study investigates a forecasting power of volatility curvatures and risk neutral densities implicit in KOSPI 200 option prices by analyzing minute by minute historical index option intraday trading data from January of 2007 to January of 2011. We begin by estimating implied volatility functions and risk neutral price densities based on non-parametric method every minute and by calculating volatility curvature and skewness premium. We then compare the daily rate of return of the signal following trading strategy that we buy (sell) a stock index when the volatility curvature or skewness premium increases (decreases) with that of an intraday buy-and-hold strategy that we buy a stock index on 9:05AM and sell it on 2:50PM. We found that the rate of return of the signal following trading strategy was significantly higher than that of the intraday buy-and-hold strategy, which implies that the option prices have a strong forecasting power on the direction of stock market. Another finding is that the information contents of option prices disappear after three or four minutes.

scholarly journals Determinants of the Forward Premium in the Nord Pool Electricity Market

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1111
Author(s):  
Erik Haugom ◽  
Peter Molnár ◽  
Magne Tysdahl
Keyword(s):  
Electricity Market ◽  
Implied Volatility ◽  
Renewable Energy Sources ◽  
Ordinary Least Squares ◽  
Spot Price ◽  
Forward Contracts ◽  
Forward Premium ◽  
Realised Volatility ◽  
The Difference ◽  
Efficient Power

Nord Pool is the leading power market in Europe. It has been documented that the forward contracts traded in this market exhibit a significant forward premium, which could be a sign of market inefficiency. Efficient power markets are important, especially when there is a goal to increase the share of the power mix stemming from renewable energy sources. We therefore contribute to the understanding of this topic by examining how the forward premium in the Nord Pool market depend on several economic and physical conditions. We utilise two methods: ordinary least squares and quantile regression. The results show that the reservoir level and the basis (the difference between the forward and spot price) have a significant impact on the forward premium. The realised volatility of futures prices and the implied volatility of the stock market have strong effects on both the conditional lower and upper tails of the forward premium. We also find that, as the market has matured, the forward premium has decreased, indicating an increase in market efficiency.

Modeling of implied volatility surfaces of nifty index options

2019 ◽  
Vol 06 (03) ◽  
pp. 1950028 ◽  
Author(s):  
Mihir Dash
Keyword(s):  
Implied Volatility ◽  
Strike Price ◽  
Index Options ◽  
Put Options ◽  
Call Options ◽  
Merton Model ◽  
Implied Volatility Surface ◽  
Black Scholes ◽  
Volatility Surface ◽  
Implied Volatility Surfaces

The implied volatility of an option contract is the value of the volatility of the underlying instrument which equates the theoretical option value from an option pricing model (typically, the Black–Scholes[Formula: see text]Merton model) to the current market price of the option. The concept of implied volatility has gained in importance over historical volatility as a forward-looking measure, reflecting expectations of volatility (Dumas et al., 1998). Several studies have shown that the volatilities implied by observed market prices exhibit a pattern very different from that assumed by the Black–Scholes[Formula: see text]Merton model, varying with strike price and time to expiration. This variation of implied volatilities across strike price and time to expiration is referred to as the volatility surface. Empirically, volatility surfaces for global indices have been characterized by the volatility skew. For a given expiration date, options far out-of-the-money are found to have higher implied volatility than those with an exercise price at-the-money. For short-dated expirations, the cross-section of implied volatilities as a function of strike is roughly V-shaped, but has a rounded vertex and is slightly tilted. Generally, this V-shape softens and becomes flatter for longer dated expirations, but the vertex itself may rise or fall depending on whether the term structure of at-the-money volatility is upward or downward sloping. The objective of this study is to model the implied volatility surfaces of index options on the National Stock Exchange (NSE), India. The study employs the parametric models presented in Dumas et al. (1998); Peña et al. (1999), and several subsequent studies to model the volatility surfaces across moneyness and time to expiration. The present study contributes to the literature by studying the nature of the stationary point of the implied volatility surface and by separating the in-the-money and out-of-the-money components of the implied volatility surface. The results of the study suggest that an important difference between the implied volatility surface of index call and put options: the implied volatility surface of index call options was found to have a minimum point, while that of index put options was found to have a saddlepoint. The results of the study also indicate the presence of a “volatility smile” across strike prices, with a minimum point in the range of 2.3–9.0% in-the-money for index call options and of 10.7–29.3% in-the-money for index put options; further, there was a jump in implied volatility in the transition from out-of-the-moneyness to in-the-moneyness, by 10.0% for index call options and about 1.9% for index put options.

Structured Products Markets and Implied Volatility Distortion

2014 ◽  
Vol 22 (3) ◽  
pp. 433-464
Author(s):  
Sun-Joong Yoon
Keyword(s):  
Financial Markets ◽  
Rapid Growth ◽  
Implied Volatility ◽  
Policy Implications ◽  
Over The Counter ◽  
Volatility Risk ◽  
Put Options ◽  
Structured Products ◽  
Payoff Structure ◽  
The Difference

This study verifies the existence of implied volatility distortion by the rapid growth of structured products such as Equity Linked Securities (ELS) in Korean financial markets and provides the policy implications to overcome such a distortion. The most ELS products issued in Korea have a step-down auto-callable payoff structure consisting of short position in down-and-in barrier put options and long position in digital call options. Financial companies which have issued ELS are exposed to the volatility risk, i.e. long vega position, and tend to execute the volatility transactions of short vega. For instance, the financial companies issue Equity-Linked Warrants or sell listed/over-the-counter vanilla options, both of which have short position in volatility risk. Accordingly, the demand for selling volatility is stronger than for buying volatility in the Korean financial markets. According to the empirical results, we conform that the rapid growth of the ELS products induces the pressure for lowering volatility and furthermore, the volatility spreads, defined as the difference between implied volatility and realized volatility, also decrease with respect the amount of the newly issued ELS. Lastly, to mitigate the volatility distortion effect, we suggest to list VKOSPI-related derivatives securities such as VKOSPI futures and options, which in turn balance the trading demands for selling and buying volatilities.

scholarly journals Too-Systemic-to-Fail: What Option Markets Imply about Sector-Wide Government Guarantees

2016 ◽  
Vol 106 (6) ◽  
pp. 1278-1319 ◽  
Author(s):  
Bryan Kelly ◽  
Hanno Lustig ◽  
Stijn Van Nieuwerburgh
Keyword(s):  
Financial Crisis ◽  
Financial Sector ◽  
Tail Risk ◽  
Option Markets ◽  
Put Options ◽  
Government Guarantee ◽  
The Difference ◽  
The Cost

We examine the pricing of financial crash insurance during the 2007–2009 financial crisis in US option markets, and we show that a large amount of aggregate tail risk is missing from the cost of financial sector crash insurance during the crisis. The difference in costs between out-of-the-money put options for individual banks and puts on the financial sector index increases four-fold from its precrisis 2003–2007 level. We provide evidence that a collective government guarantee for the financial sector lowers index put prices far more than those of individual banks and explains the increase in the basket-index put spread. (JEL E44, G01, G13, G21, G28, H81)

Deviations from Put-Call Parity and Stock Return Predictability

2010 ◽  
Vol 45 (2) ◽  
pp. 335-367 ◽  
Author(s):  
Martijn Cremers ◽  
David Weinbaum
Keyword(s):  
Stock Returns ◽  
Implied Volatility ◽  
Option Prices ◽  
Stock Return Predictability ◽  
Put Options ◽  
Short Sale Constraints ◽  
Short Sale ◽  
The Difference ◽  
Underlying Stocks ◽  
Abnormal Performance

AbstractDeviations from put-call parity contain information about future stock returns. Using the difference in implied volatility between pairs of call and put options to measure these deviations, we find that stocks with relatively expensive calls outperform stocks with relatively expensive puts by 50 basis points per week. We find both positive abnormal performance in stocks with relatively expensive calls and negative abnormal performance in stocks with relatively expensive puts, which cannot be explained by short sale constraints. Rebate rates from the stock lending market directly confirm that our findings are not driven by stocks that are hard to borrow. The degree of predictability is larger when option liquidity is high and stock liquidity low, while there is little predictability when the opposite is true. Controlling for size, option prices are more likely to deviate from strict put-call parity when underlying stocks face more information risk. The degree of predictability decreases over the sample period. Our results are consistent with mispricing during the earlier years of the study, with a gradual reduction of the mispricing over time.

Financial Crisis, Put-Call Parity and Momentum Effect

2014 ◽  
Vol 22 (1) ◽  
pp. 141-159
Author(s):  
Suhkyong Kim
Keyword(s):  
Financial Crisis ◽  
Stock Prices ◽  
Trading Volume ◽  
Least Square ◽  
Options Market ◽  
Momentum Effect ◽  
Put Options ◽  
Crisis Period ◽  
Short Sale ◽  
Futures Price

This study investigates the deviation from put-call parity in the KOSPI200 options market. The sample period is from January 2, 2006 to May 31, 2009. Due to the financial crisis in 2008, short sale of stocks had been prohibited from October 1, 2008 to May 31, 2009. The sample is divided into the pre-crisis period and the crisis period. The crisis period is the period during which short sale of stocks are prohibited. The summary statistics shows that the trading volume of KOSPI200 stocks doubled, but the trading volume of call options and that of put options declined to one half and one third from the pre-crisis period to the crisis period, respectively. The equation which relates the deviation of futures price to the deviation of put-call parity is derived and the deviation from put-call parity is analyzed by using two stage least square. This paper looks into not only the prior 60 day return's momentum effect, but also the intraday spot return's momentum effect. Evidence indicates that the intraday momentum does exist in options and stock prices. Empirical results show that the prior 60 day return's momentum effect is statistically insignificant during the pre-crisis period, but statistically significant during the crisis period whereas the intraday return's momentum effect is strongly significant for both of the periods. This result lends support to the argument that the deviation of futures price from its theoretical price is a component of the deviation from put-call parity. The sign and significance of the regression coefficient for momentum effects are consistent with Kim and Park (2011) and Kim (2012) again lending support to the validity of their regression equation. Overall, our results are consistent with the validity of the derived equation, Kim and Park (2011) and Kim (2013)’s rationale.

scholarly journals Delta-gamma-theta Hedging of Crude Oil Asian Options

2015 ◽  
Vol 63 (6) ◽  
pp. 1897-1903
Author(s):  
Juraj Hruška
Keyword(s):  
Market Price ◽  
Options Pricing ◽  
Exotic Options ◽  
Asian Options ◽  
Hedging Strategy ◽  
Strike Price ◽  
Put Options ◽  
Hedging Strategies ◽  
Black Scholes ◽  
The Difference

Since Black-Scholes formula was derived, many methods have been suggested for vanilla as well as exotic options pricing. More of investing and hedging strategies have been developed based on these pricing models. Goal of this paper is to derive delta-gamma-theta hedging strategy for Asian options and compere its efficiency with gamma-delta-theta hedging combined with predictive model. Fixed strike Asian options are type of exotic options, whose special feature is that payoff is calculated from the difference of average market price and strike price for call options and vice versa for the put options. Methods of stochastic analysis are used to determine deltas, gammas and thetas of Asian options. Asian options are cheaper than vanilla options and therefore they are more suitable for precise portfolio creation. On the other hand their deltas are also smaller as well as profits. That means that they are also less risky and more suitable for hedging. Results, conducted on chosen commodity, confirm better feasibility of Asian options compering with vanilla options in sense of gamma hedging.

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