Coarse Thinking, Implied Volatility, and the Price of Call and Put Options

2010 ◽  
Author(s):  
Hammad Siddiqi
Keyword(s):  
Implied Volatility ◽  
Put Options

Can Derivative Information Predict Stock Price Jumps?

2015 ◽  
Vol 31 (3) ◽  
pp. 845
Author(s):  
Noe-Keol Kwark ◽  
Hyoung-Goo Kang ◽  
Sang-Gyung Jun
Keyword(s):  
Standard Deviation ◽  
Exchange Rates ◽  
Stock Prices ◽  
Stock Price ◽  
Implied Volatility ◽  
Stock Index ◽  
Rates Of Return ◽  
Cross Sectional ◽  
Put Options ◽  
The Cross

<p>This study examines the predictability of jumps in stock prices using options-trading information, the futures basis spread, the cross-sectional standard deviation of returns on components in the stock index, and exchange rates. A stock price jump was defined as a large fluctuation in the stock price that deviated from the distribution thresholds of the past rates of return. This empirical analysis shows that the implied volatility spread between ATM call and put options was a significant predictor for both upward and downward jumps, whereas the volatility skew was less significant. In addition, the futures basis spread was moderately significant for downward stock price jumps. Both the cross-sectional standard deviation of the rates of return on component stocks in the KOSPI 200 and the won-dollar exchange rates were significant predictors for both upward and downward jumps.</p>

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.

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.

ASYMPTOTIC APPROXIMATIONS FOR PRICING DERIVATIVES UNDER MEAN-REVERTING PROCESSES

2016 ◽  
Vol 19 (05) ◽  
pp. 1650030 ◽  
Author(s):  
RICHARD JORDAN ◽  
CHARLES TIER
Keyword(s):  
Interest Rates ◽  
Implied Volatility ◽  
Asymptotic Approximations ◽  
Ray Method ◽  
Interest Rate Derivatives ◽  
Put Options ◽  
Merton Model ◽  
Volatility Model ◽  
Black Scholes ◽  
Efficient Alternative

The problem of fast pricing, hedging, and calibrating of derivatives is considered when the underlying does not follow the standard Black–Scholes–Merton model but rather a mean-reverting and deterministic volatility model. Mean-reverting models are often used for volatility, commodities, and interest-rate derivatives, while the deterministic volatility accounts for the nonconstant implied volatility. Trading desks often use numerical methods for real-time pricing, hedging, and calibration when implementing such models. A more efficient alternative is to use an analytic formula, even if only approximate. A systematic approach is presented, based on the WKB or ray method, to derive asymptotic approximations to the density function that can be used to derive simple formulas for pricing derivatives. Such approximations are usually only valid away from any boundaries, yet for some derivatives the values of the underlying near the boundaries are needed such as when interest rates are very low or for pricing put options. Hence, the ray approximation may not yield acceptable results. A new asymptotic approximation near boundaries is derived, which is shown to be of value for pricing certain derivatives. The results are illustrated by deriving new analytic approximations for European derivatives and their high accuracy is demonstrated numerically.

scholarly journals The Behavior of Option’s Implied Volatility Index: a Case of India VIX

2015 ◽  
Vol 16 (2) ◽  
pp. 149-158 ◽  
Author(s):  
Imlak Shaikh ◽  
Puja Padhi
Keyword(s):  
Implied Volatility ◽  
Negative Impact ◽  
Practical Implication ◽  
Stock Market Volatility ◽  
Put Options ◽  
Monday Effect ◽  
Volatility Index ◽  
Significant Negative Impact ◽  
Day Of The Week ◽  
India Vix

The aim of this paper is to investigate the behavior of implied volatility in the form of day-of-the-week, year-of-the-month and surround the expiration of options. The persistence of volatility is modeled in ARCH/GARCH type framework. The empirical results have shown significant effects of the day-of-the-week, month-of-the-year and day of options expiration. The positive significant Monday effect explains that India VIX rises significantly on the initial days of the market opening, and the significant negative Wednesday effect shows that expected stock market volatility fall through Wednesday-Friday. Moreover, the study reveals the fact on options expiration, the evidence shows that India VIX fall significantly on the day of expiration of European call and put options. The March and December months have reported significant negative impact on the volatility index. Certainly, this kind of results holds practical implication for volatility traders, and helps to the market participant in hedging and pricing of options.

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.

Behaviour and determinants of implied volatility in Indian market

2016 ◽  
Vol 13 (3) ◽  
pp. 271-291 ◽  
Author(s):  
Narain ◽  
Narander Kumar Nigam ◽  
Piyush Pandey
Keyword(s):  
Implied Volatility ◽  
Hedge Fund ◽  
International Study ◽  
Volatility Smile ◽  
Vector Autoregressions ◽  
Index Options ◽  
Content Type ◽  
Put Options ◽  
Fund Managers ◽  
Option Contract

Purpose The purpose of this paper is to understand the patterns of the implied volatility (IV) of the Indian index option market and its relationship with moneyness (called the volatility smile). Its goal is also to ascertain the determinants of IV. Design/methodology/approach For this purpose, IVs were computed from the daily call and put data of CNX Nifty index options from April 2004 to March 2014. The patterns of IVs were analysed using univariate parametric tests. Multivariate regression analyses were conducted to understand the relationships observed. Resultantly, vector autoregressions were performed to assess the determinants of IV. Findings The results suggested that there was asymmetric volatility across time and strike prices using alternative measures of moneyness. Furthermore, it was found that the IV of lower strike prices was significantly higher (lower) than that of higher strike prices for call (put) options. Put IV was observed to be higher than call IV irrespective of any attributes. The results further showed that current-month contracts have significantly higher IV than those for next month and those were followed by far-month contracts. Nifty futures’ volumes and momentum were found to be significant determinants of IV. Practical implications The behaviour of the volatility smile is important when accounting for the Vega risks in the portfolios of hedge fund managers. While taking a position, besides the Black-Scholes-Merton (BSM) model’s input factors, investors must consider the previous behaviour of volatility, a market’s microstructures and its liquidity for a put option contract. They must also consider the attributes of the underlying for a call option contract. Originality/value This is the first decadal study (the longest span of data for any international study on this subject) to confirm the existence of the volatility smile for the index options market in India. It examines and confirms the smile’s asymmetry patterns for different definitions of moneyness, as well as option types, the tenure of options contracts and the different phases of market conditions. It further helps to identify the determinants of IV and so has renewed importance for traders.

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.

Which Option Pricing Model Is the Best? HF Data for Nikkei 225 Index Options

2019 ◽  
Vol 4 (51) ◽  
pp. 18-39
Author(s):  
Kokoszczyński Ryszard ◽  
Sakowski Paweł ◽  
Ślepaczuk Robert
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Model Performance ◽  
Stochastic Volatility Model ◽  
Percentage Error ◽  
Pricing Models ◽  
Index Options ◽  
Put Options ◽  
Pricing Errors ◽  
Volatility Model

Abstract In this study, we analyse the performance of option pricing models using 5-minutes transactional data for the Japanese Nikkei 225 index options. We compare 6 different option pricing models: the Black (1976) model with different assumptions about the volatility process (realized volatility with and without smoothing, historical volatility and implied volatility), the stochastic volatility model of Heston (1993) and the GARCH(1,1) model. To assess the model performance, we use median absolute percentage error based on differences between theoretical and transactional options prices. We present our results with respect to 5 classes of option moneyness, 5 classes of option time to maturity and 2 option types (calls and puts). The Black model with implied volatility (BIV) comes as the best and the GARCH(1,1) as the worst one. For both call and put options, we observe the clear relation between average pricing errors and option moneyness: high error values for deep OTM options and the best fit for deep ITM options. Pricing errors also depend on time to maturity, although this relationship depend on option moneyness. For low value options (deep OTM and OTM), we obtained lower errors for longer maturities. On the other hand, for high value options (ITM and deep ITM) pricing errors are lower for short times to maturity. We obtained similar average pricing errors for call and put options. Moreover, we do not see any advantage of much complex and time-consuming models. Additionally, we describe liquidity of the Nikkei225 option pricing market and try to compare the results we obtain here with a detailed study for Polish emerging option market (Kokoszczyński et al. 2010b).

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.

Sign in / Sign up

Export Citation Format

Share Document