Coherent Model-Free Implied Volatility: A Corridor Fix for High-Frequency VIX

2011 ◽  
Author(s):  
Torben G. Andersen ◽  
Oleg Bondarenko ◽  
Maria T. Gonzalez-Perez
Keyword(s):  
High Frequency ◽  
Implied Volatility ◽  
Model Free

Implied volatility smirk and future stock returns: evidence from the German market

2015 ◽  
Vol 41 (12) ◽  
pp. 1357-1379
Author(s):  
Di Mo ◽  
Neda Todorova ◽  
Rakesh Gupta
Keyword(s):  
High Frequency ◽  
Implied Volatility ◽  
Stock Index ◽  
High Frequency Data ◽  
Frequency Data ◽  
European Options ◽  
German Market ◽  
Content Type ◽  
The Relationship ◽  
Option Market

Purpose – The purpose of this paper is to investigate the relationship between option’s implied volatility smirk (IVS) and excess returns in the Germany’s leading stock index Deutscher-Aktien Index (DAX) 30. Design/methodology/approach – The study defines the IVS as the difference in implied volatility derived from out-of-the-money put options and at-the-money call options. This study employs the ordinary least square regression with Newey-West correction to analyse the relationship between IVS and excess DAX 30 index returns in Germany. Findings – The authors find that the German market adjusts information in an efficient way. Consequently, there is no information linkage between option volatility smirk and market index returns over the nine years sample period after considering the control variables, global financial crisis dummies, and the subsample test. Research limitations/implications – This study finds that the option market and the DAX 30 index are informationally efficient. Implications of the findings are that the investors cannot profit from the information contained in the IVS since the information is simultaneously incorporated into option prices and the stock index prices. The findings of this study are applicable to other markets with European options and for market participants who seek to exploit short-term market divergence from efficiency. Originality/value – The relationship between IVS and stock price changes has not been investigated sufficiently in academic literature. This study looks at this relationship in the context of European options using high-frequency transactions data. Prior studies look at this relationship for only American options using daily data. Pricing efficiency of the European option market using high-frequency data have not been studied in the prior literature. The authors find different results for the German market based on this high-frequency data set.

scholarly journals Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 30
Author(s):  
Fabien Le Floc’h ◽  
Cornelis Oosterlee
Keyword(s):  
Implied Volatility ◽  
Initial Guess ◽  
Stochastic Collocation ◽  
Option Prices ◽  
Spline Collocation ◽  
Model Free ◽  
Free Interpolation ◽  
Collocation Technique ◽  
Interpolation Technique ◽  
The Stability

This paper explores the stochastic collocation technique, applied on a monotonic spline, as an arbitrage-free and model-free interpolation of implied volatilities. We explore various spline formulations, including B-spline representations. We explain how to calibrate the different representations against market option prices, detail how to smooth out the market quotes, and choose a proper initial guess. The technique is then applied to concrete market options and the stability of the different approaches is analyzed. Finally, we consider a challenging example where convex spline interpolations lead to oscillations in the implied volatility and compare the spline collocation results with those obtained through arbitrage-free interpolation technique of Andreasen and Huge.

An Empirical Research on the Informational Efficiency of Model Free Implied Volatility

2008 ◽  
Vol 16 (2) ◽  
pp. 67-94
Author(s):  
Byung Kun Rhee ◽  
Sang Won Hwang
Keyword(s):  
Implied Volatility ◽  
Realized Volatility ◽  
Informational Efficiency ◽  
Option Prices ◽  
Index Options ◽  
Model Free ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Korean Market ◽  
Better Than

Black-Scholes Imolied volatility (8SIV) has a few drawbacks. One is that the model Is not much successful in fitting the option prices. and It Is n야 guaranteed the model is correct one. Second. the usual tradition in using the BSIV is that only at-the-money Options are used. It is well-known that IV's of In-the-money or Qut-of-the-money ootions are much different from those estimated from near-the-money options. In this regard, a new model is confronted with Korean market data. Brittenxmes and Neuberger (2000) derive a formula for volatility which is a function of option prices‘ Since the formula is derived without using any option pricing model. volatility estimated from the formula is called model-tree implied volatillty (MFIV). MFIV overcomes the two drawbacks of BSIV. Jiang and Tian (2005) show that. with the S&P index Options (SPX), MFIV is suoerlor to historical volatility (HV) or BSIV in forecasting the future volatllity. In KOSPI 200 index options, when the forecasting performances are compared, MFIV is better than any other estimated volatilities. The hypothesis that MFIV contains all informations for realized volatility and the other volatilities are redundant is oot rejected in any cases.

Information Content of Adjusted Implied Volatility in the KOSPI 200 Index Options Market

2009 ◽  
Vol 17 (4) ◽  
pp. 75-103
Author(s):  
Byung Jin Kang ◽  
Sohyun Kang ◽  
Sun-Joong Yoon
Keyword(s):  
Implied Volatility ◽  
Risk Premia ◽  
Risk Averse ◽  
Options Market ◽  
Jump Risk ◽  
Index Options ◽  
Volatility Risk ◽  
Model Free ◽  
Volatility Model ◽  
Forecasting Errors

This study examines the forecasting ability of the adjusted implied volatility (AIV), which is suggested by Kang, Kim and Yoon (2009), using the horserace competition with historical volatility, model-free implied volatility, and BS implied volatility in the KOSPI 200 index options market. The adjusted implied volatility is applicable when investors are not risk averse or when underlying returns do not follow a normal distribution. This implies that AIV is consistent with the presence of risk premia for other risk such as volatility risk and jump risk. Using KOSPI 200 index options, it is shown that the AIV outperforms other volatility estimates in terms of the unbiasedness for future realized volatilities as well as the forecasting errors.

MODEL-FREE IMPLIED VOLATILITY: FROM SURFACE TO INDEX

2011 ◽  
Vol 14 (04) ◽  
pp. 433-463 ◽  
Author(s):  
M. FUKASAWA ◽  
I. ISHIDA ◽  
N. MAGHREBI ◽  
K. OYA ◽  
M. UBUKATA ◽  
...  
Keyword(s):  
Implied Volatility ◽  
Asset Price ◽  
Quadratic Variation ◽  
Stochastic Volatility Model ◽  
Model Free ◽  
Volatility Index ◽  
Implied Volatility Surface ◽  
Volatility Model ◽  
Pricing Measure ◽  
Volatility Surface

We propose a new method for approximating the expected quadratic variation of an asset based on its option prices. The quadratic variation of an asset price is often regarded as a measure of its volatility, and its expected value under pricing measure can be understood as the market's expectation of future volatility. We utilize the relation between the asset variance and the Black-Scholes implied volatility surface, and discuss the merits of this new model-free approach compared to the CBOE procedure underlying the VIX index. The interpolation scheme for the volatility surface we introduce is designed to be consistent with arbitrage bounds. We show numerically under the Heston stochastic volatility model that this approach significantly reduces the approximation errors, and we further provide empirical evidence from the Nikkei 225 options that the new implied volatility index is more accurate in predicting future volatility.

scholarly journals VOLATILITY DERIVATIVES AND MODEL-FREE IMPLIED LEVERAGE

2014 ◽  
Vol 17 (01) ◽  
pp. 1450002 ◽  
Author(s):  
MASAAKI FUKASAWA
Keyword(s):  
Implied Volatility ◽  
Asset Price ◽  
Simple Relation ◽  
Heston Model ◽  
Model Free ◽  
Implied Volatility Surface ◽  
Black Scholes ◽  
Volatility Derivatives ◽  
Quadratic Covariation ◽  
Volatility Surface

We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract on the quadratic covariation between an asset price and the model-free implied variance (MFIV) of the asset. It can be replicated in a model-free manner and its fair strike may be interpreted as a model-free measure for the covariance of the asset price and the realized variance. The fair strike is given in a remarkably simple form, which enable to compute it from the Black–Scholes implied volatility surface. We call it the model-free implied leverage (MFIL) and give several characterizations. In particular, we show its simple relation to the Black–Scholes implied volatility skew by an asymptotic method. Further to get an intuition, we demonstrate some explicit calculations under the Heston model. We report some empirical evidence from the time series of the MFIV and MFIL of the Nikkei stock average.

FORWARD AND FUTURE IMPLIED VOLATILITY

2011 ◽  
Vol 14 (03) ◽  
pp. 407-432 ◽  
Author(s):  
PAUL GLASSERMAN ◽  
QI WU
Keyword(s):  
Implied Volatility ◽  
Transition Density ◽  
Option Prices ◽  
Piecewise Constant ◽  
Model Based ◽  
Model Free ◽  
Out Of Sample ◽  
Sabr Model ◽  
Using Data ◽  
Better Than

We address the problem of defining and calculating forward volatility implied by option prices when the underlying asset is driven by a stochastic volatility process. We examine alternative notions of forward implied volatility and the information required to extract these measures from the prices of European options at fixed maturities. We then specialize to the SABR model and show how the asymptotic expansion of the bivariate transition density in Wu (forthcoming) allows calibration of the SABR model with piecewise constant parameters and calculation of forward volatility. We then investigate empirically whether current option prices at multiple maturities contain useful information in predicting future option prices and future implied volatility. We undertake this investigation using data on options on the euro-dollar, sterling-dollar, and dollar-yen exchange rates. We find that prices across maturities do indeed have predictive value. Moreover, we find that model-based forward volatility extracts this predicative information better than a standard "model-free" measure of forward volatility and better than spot implied volatility. The enhancement to out-of-sample forecasting accuracy gained from model-based forward volatility is greatest at longer forecasting horizons.

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