Volatility Implied by Option Prices: The Case of Takeover Bids

We model the effect of an impending share price jump on the implied standard deviation (ISD) of a company's options, testing the model by investigating its predictive ability for ISDs of companies subject to a takeover bid. Our model fits the observed ISDs well for all but certain deep in-the-money options. However, the model demonstrates that a discontinuity in the relationship between moneyness and the ISD both explains the combination of high and zero ISDs exhibited by these options, and impairs the predictive power of the model at these levels of moneyness.     

Binomial Option Pricing Biases and Inconsistent Implied Volatilities

We evaluate the binomial option pricing methodology (OPM) by examining simulated portfolio strategies. A key aspect of our study involves sampling from the empirical distribution of observed equity returns. Using a Monte Carlo simulation, we generate equity prices under known volatility and return parameters. We price American–style put options on the equity and evaluate the risk–adjusted performance of various strategies that require writing put options with different maturities and moneyness characteristics. The performance of these strategies is compared to an alternative strategy of investing in the underlying equity. The relative performance of the strategies allows us to identify biases in the binomial OPM leading to the well–known volatility smile . By adjusting option prices so as to rule out dominated option strategies in a mean–variance context, we are able to reduce the pricing errors of the OPM with respect to option prices obtained from the LIFFE. Our results suggest that a simple recalibration of inputs may improve binomial OPM performance.     

A Note on the Term Structure of Implied Volatilities for the Yen/U.S. Dollar Currency Option

This paper tests the relationship between short dated and long dated implied volatilities obtained from Tokyo market currency option prices by employing three different volatility models: a mean reverting model, a GARCH model, and an EGARCH model. We document evidence that long dated average expected volatility is higher than that predicted by the term structure relationship during the dramatic appreciation of yen/dollar exchange in the early 1990's. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Dynamics of the S&P 500 Implied Volatility Surface

This empirical study is motivated by the literature on “smile-consistent” arbitrage pricing with stochastic volatility. We investigate the number and shape of shocks that move implied volatility smiles and surfaces by applying Principal Components Analysis. Two components are identified under a variety of criteria. Subsequently, we develop a “Procrustes” type rotation in order to interpret the retained components. The results have implications for both option pricing and hedging and for the economics of option pricing. This revised version was published online in June 2006 with corrections to the Cover Date.     

Implied Standard Deviations and Post-earnings Announcement Volatility

This paper investigates volatility increases following annual earnings announcements. Standard deviations implied by options prices are used to show that announcements of bad news result in a lower volatility increase than those of good news, and delay the increase by a day. Reports that are difficult to interpret also delay the volatility increase. This delay is incremental to that caused by reporting bad news, although the effect of bad news on slowing down the reaction time is dominant. It is argued that the delays reflect market uncertainty about the implications of the news.     

Option Prices Under Generalized Pricing Kernels

In this paper analytical solutions for European option prices are derived for a class of rather general asset specific pricing kernels (ASPKs) and distributions of the underlying asset. Special cases include underlying assets that are lognormally or log-gamma distributed at expiration date T. These special cases are generalizations of the Black and Scholes (1973) option pricing formula and the Heston (1993) option pricing formula for non-constant elasticity of the ASPK. Analytical solutions for a normally distributed and a uniformly distributed underlying are also derived for the class of general ASPKs. The shape of the implied volatility is analyzed to provide further understanding of the relationship between the shape of the ASPK, the underlying subjective distribution and option prices. The properties of this class of ASPKs are also compared to approaches used in previous empirical studies. JEL Classification: G12, G13, C65 Erik Lüders is an assistant professor at Laval University and a visiting scholar at the Stern School of Business, New York University.     

A Note on Computation of Implied Volatility

This is a note on computation of the implied volatility in theBlack–Scholes formula to evaluate an accuracy of the computation.     

投资者情绪、期权隐含信息与股市波动率预测——基于上证50ETF期权的经验研究

在异质自回归模型(HAR-RV)中引入中国上证50ETF期权隐含信息和投资者情绪,本文分别对中国股票市场未来日、周和月波动率进行预测。研究发现,期权隐含信息和投资者情绪能够提高HAR-RV模型对股票市场未来波动率的预测效果。投资者情绪对未来波动率的影响存在两种机制:在情绪高涨期间,月已实现波动率与未来波动率正相关,说明以个人投资者占主体所引起的价格信息机制,在中国股票市场交易中占主导作用;风险中性偏度与未来波动率负相关,说明以个人投资者占主体所引起的噪声交易机制占主导作用。     

Expectations Hypothesis of the Term Structure of Implied Volatility: Evidence from Foreign Currency and Stock Index Options

Using a stochastic volatility option pricing model, we showthat the implied volatilities of at-the-money options are notnecessarily unbiased and that the fixed interval time-seriescan produce misleading results. Our results do not support theexpectations hypothesis: long-term volatilities rise relativeto short-term volatilities, but the increases are not matchedas predicted by the expectations hypothesis. In addition, anincrease in the current long-term volatility relative to thecurrent short-term volatility is followed by a subsequent decline.The results are similar for both foreign currency and the S&P500 stock index options.     

Intra–day Behavior of Treasury Sector Index Option Implied Volatilities around Macroeconomic Announcements

If option implied volatility is an unbiased, efficient forecast of future return volatility in the underlying asset, then we should be able to predict its path around macroeconomic announcements from responses in cash markets. Regressions show that volatilities rise the afternoon before announcements that move cash markets, and that post–announcement volatilities return to normal as rapidly as cash prices do. Although implied volatilities are predictable, the Treasury options market is efficient since informed traders do not earn arbitrage profits once we account for trading costs.     

Option Implied Dividends Predict Dividend Cuts: Evidence from the Financial Crisis

We employ the forward‐looking implied dividend information contained in option prices to predict dividend cuts and omissions during the recent financial crisis. The large number of dividend cuts and omissions during the 2008–09 financial crisis period provides the opportunity to study the predictability of dividend cuts in a controlled environment. Implied dividends and implied volatility, based on put–call parity and computed from put and call option prices, prove to be effective in predicting those cuts, especially compared to only using the equity market and accounting variables conventionally used for this purpose. Options‐derived variables (implied dividends and implied volatility) enhance the ability to identify firms more likely to reduce or omit dividend payments.     

Implied Volatility of Interest Rate Options: An Empirical Investigation of the Market Model

We analyze the empirical properties of the volatilityimplied in options on the 13-week US Treasury bill rate. These options havenot been studied previously. It is shown that a European style put optionon the interest rate is equivalent to a call option on a zero-coupon bond.We apply the LIBOR market model and conduct a battery of validity tests tocompare three different volatility specifications: contact, affine, and exponentialvolatility. It appears that the additional parameter in the affine and theexponential volatility function is not justified. Overall, the LIBOR marketmodel fares well in describing these options.     

Implied Volatility in the U.K. Commercial Property Market: Empirical Evidence Based on Transaction Data

The primary aim of this research is to compute implied volatility based on a stochastic contingent claim valuation model proposed by Dixit and Pindyck (1994). Over the sample period of 1984 to 1997, and with approximately 20,000 commercial property transactions in the United Kingdom, we find that implied volatility of rental returns is in the region of 24.83 percent. Over the same sample period, the historical and conditional standard deviations of the log returns of transaction-based rental series is estimated to be 15.60 percent and 35.64 percent, respectively. The tests of information content of these risk measures show that there is strong orthogonality in the information impounded in implied volatility estimates compared to that contained in historical standard deviations.     

Option Bounds and the Pricing of the Volatility Smile

This paper presents a new approach forthe estimation of the risk-neutral probability distribution impliedby observed option prices in the presence of a non-horizontalvolatility smile. This approach is based on theoretical considerationsderived from option pricing in incomplete markets. Instead ofa single distribution, a pair of risk-neutral distributions areestimated, that bracket the option prices defined by the volatilitybid/ask midpoint. These distributions define upper and lowerbounds on option prices that are consistent with the observableoption parameters and are the tightest ones possible, in thesense of minimizing the distance between the option upper andlower bounds. The application of the new approach to a sampleof observations on the S&P 500 option market showsthat the bounds produces are quite tight, and also that theirderivation is robust to the presence of violations of arbitragerelations in option quotes, which cause many other methods tofail.     

On the Distribution of CBOE Option Trade Prices Occurring Between Consecutive Stock Trades

This paper examines the volume distribution of option trade prices that occurs when the underlying stock price remains constant. The width of these option trade price bands provides direct evidence on the law of one price and the redundancy of options assumed in many option models. We find that index option bands are narrower than equity option bands. Furthermore, for both equity and index options, puts have narrower bandwidths than calls. In general, option price bandwidth is narrow and can be explained by the minimum price movement allowed by the Chicago Board Options Exchanges (CBOE). This supports the single price law and the redundancy assumption. The existence of bid/ask quotes on the option does not materially affect the above results although it does alter the frequency of multiple option trade prices for a given underlying stock price. We note that over 53% of option trading volume occurs without bid/ask quotes on the CBOE compared to less than 15% a decade ago. Our results suggest that the effective bid/ask spread on options is probably no larger than the minimum price movements allowed by the CBOE. Furthermore, the need for the liquidity services of market makers may be declining if the decline in quoting activity stems from cross trading (i.e. trades not involving market makers).     

Modelling the Implied Volatility of Options on Long Gilt Futures

This paper investigates the properties of implied volatility series calculated from options on Treasury bond futures, traded on LIFFE. We demonstrate that the use of near-maturity at the money options to calculate implied volatilities causes less mis-pricing and is therefore superior to, a weighted average measure encompassing all relevant options. We demonstrate that, whilst a set of macroeconomic variables has some predictive power for implied volatilities, we are not able to earn excess returns by trading on the basis of these predictions once we allow for typical investor transactions costs.     

国内外石油价格波动性溢出效应研究

本文分析了国内外石油价格波动传导机制与国内外石油价格波动的典型化事实 ,将动态相关系数的多变量随机波动模型与固定系数的Granger波动性因果关系模型结合起来,构建了动态相关系数的带Granger因果检验的多元随机波动模型(DGC-MSV),并实证检验了美国、英国和中国的石油现货价格之间、期货价格之间以及期货价格与现货价格之间的波动溢出效应,主要得到如下结论:中国、美国、英国石油期货价格、现货价格波动性之间的相关系数都是动态变化的;中国石油现货价格受美国石油现货价格的波动溢出影响,而同时中国石油现货价格又对美国和英国的石油期货价格波动有显著溢出效应;英国和美国的石油现货价格之间、石油期货价格之间都具有双向波动溢出效应;中国石油市场的金融属性低于英国和美国石油市场。最后提出一些对策建议。     

Regime-Dependent Relationships Between the Implied Volatility Index and Stock Market Index

We examine regime-dependent dynamics between Korea's representative implied volatility index (VKOSPI) and stock market index (KOSPI 200) using a two-regime threshold vector error correction model (TVECM). By analyzing high-quality daily data from January 2003 to June 2013, we make the following interesting observations based on a model with regime splitting. First, regardless of regime, we observe a negative contemporaneous correlation between the VKOSPI and KOSPI 200. Second, while the KOSPI 200 generally leads the VKOSPI under normal market conditions (lower regime), this relationship is overturned when market volatility measured by the VKOSPI level is extremely high (upper regime). Third, in the TVECM framework, the effects of lagged VKOSPI on the KOSPI 200 are positive only in the upper regime, while the effects of lagged KOSPI 200 on the VKOSPI are positive only in the lower regime; this cannot be explained by the traditional framework of an asymmetric volatility phenomenon. Fourth, the KOSPI 200 exhibits greater sensitivity to implied volatility shocks in the upper regime than it does to those in the lower regime.     

A Non-Parametric Option Pricing Model: Theory and Empirical Evidence

In this paper, we propose an empirically-based, non-parametric option pricing model to evaluate S&P 500 index options. Given the fact that the model is derived under the real measure, an equilibrium asset pricing model, instead of no-arbitrage, must be assumed. Using the histogram of past S&P 500 index returns, we find that most of the volatility smile documented in the literature disappears.