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Abstract:
It is well known that finding an accurate forecast of future volatility turns out to be very useful for pricing derivatives, hedging strategies or for the calculation of the Value at Risk. The market's assessment of the underlying asset's volatility as reflected in the option price is known as the implied volatility of the option. Based on teaching derived from these recent papers written on the forecasting ability of implied volatility, this paper deals with the accuracy of international volatility indexes (VX1, VDAX and VIX). First, we find that VX1, VIX and VDAX are good tools for predicting future realized volatility and we also show that past implied volatility informs more about future implied volatility than past realized volatility. We, also, embed each of the implied volatility indexes as an exogenous term in the GARCH variance equation and find that all of them dominates the GARCH terms. Second, We also compute parameters of a stochastic volatility model using implied volatility indexes. Third, we study the transmission mechanisms of implied volatility indexes.

GARCH model, Implied Volatility Index, Risk Management

Abstract:
Corrado and Su (1998) implemented the stochastic volatility model of Hull and White (1988) for a particular case where variance is equal to its long-term mean. This note provides a slight correction to the series expansion derived by Corrado and Su (1998) and proposes a simulation to display the effect of this error.

Abstract:
The relation between risk and return is very well documented in financial literature. While Sharpe (1964) proposed a linear relation between risk and return through the CAPM, Black (1976) pointed out later an asymmetric relation between these variables. Indeed, he noted that volatility was higher after a stock market fall than after a rise. From this observation, many articles were written on the transmission mechanism of price and on volatility spillovers across different markets. All these papers modeled returns and historical variance through different models and generally with GARCH models.

In this paper, we propose a precise description of volatility spillovers based on the international transmission of implied volatility. Indeed, we examine the possible interactions between returns and implied volatility and between implied volatilities belonging to different markets. To do so, we use three implied volatility indexes, the French VX1, the German VDAX and the American VIX.

We find very interesting results concerning the impact of news on the implied volatility behavior and also on the interaction between implied volatility and realized volatility. We get rich information on the nature of the underlying process of implied volatility and historical volatility.

GARCH model, Implied Volatility, Risk Management

Abstract:
This article is an empirical study dedicated to the GARCH Option pricing model of Duan (1995) applied to the FTSE 100 European style options for various maturities. The beauty of this model is in that it used the standard GARCH theory in an option perspective and also in its flexibility to adapt to different rich GARCH specifications. We analyze the validity of the model given its ability to price one-day ahead out-of-sample call options and also its ability to capture the empirical dynamic of the volatility skew.

We get severe mispricing for deep out-of-the-money and short term call options, which tend to decrease the global performance of the model that is relatively correct. We note that long term skews tend to be more stable across time and strikes, which explains why we had a decreasing pricing bias for longer maturity contracts. We also get that skews tend to deform into smiles as we go toward the expiry date. This model reveals a good ability to capture the change of regime in the implied volatility surface judging from the transformation observed from smiles to skews.

Abstract:
This paper presents a capital asset pricing model in the presence of asymmetric information and transaction costs. The model is a generalized version of Merton's (1987) model and Black's (1974) model. Empirical tests show a negative relation between the expected rate of return and the shadow costs of incomplete information. The results in this paper have the potential to explain the home bias equity in a domestic and an international context.

Abstract:
The mispricing of the deep-in-the money and deep-out-the-money generated by the Black-Scholes (1973) model is now well documented in the literature. In this paper, we discuss different option valuation models on the basis of empirical tests carry out on the French option market. We examine methods that account for non-normal skewness and kurtosis, relax the martingale restriction, mix two log-normal distributions, and allows either for jump diffusion process or for stochastic volatility. We find that the use of a jump diffusion and stochastic volatility model performs as well as the inclusion of non normal skewness and kurtosis in terms of precision in the option valuation.

Keywords : Implied Volatility, Stochastic Volatility Model, Jump Diffusion Model, Skewness, Kurtosis

Abstract:
Dependence is an important issue in credit risk portfolio modeling and pricing. We discuss a straightforward common factor model of credit risk dependence, which is motivated by intensity models such as Duffie and Singleton (1998), among others. In the empirical analysis, we study dependence under the risk-neutral measure using credit default swap (CDS) spread data of liquid large-cap U.S. obligors. The proxy for the common factor is the DJ CDX.NA.IG index. We document that (i) the CDX factor is significant but has low explanatory power, (ii) factor sensitivities show distinct time-varying nature and that (iii) systematic credit risk shows asymmetric extreme factor dependence, where extreme dependence is present for upward CDX movements only. This finding from an EVT-copula approach is what is predicted by various intensity models of joint defaults.

credit risk, factor model, time-varying risk, extreme dependence

Abstract:
The market's assessment of the underlying asset's volatility as reflected in the option price is known as the implied volatility. Implied volatility indexes were created with the idea to provide an investor fear gauge since they represent a forecast of future average volatility. This article compares the behavior of three implied volatility indexes, the US VIX, the German VDAX and the French VX1.It empirically showed that the VX1 index tends to exagerate the volatility of the French market.

Implied volatility

Abstract:
The failure of the Black-Scholes (1973) model is now well documented in the literature. In this article, we discuss two alternative option valuation models whose volatility follows a stochastic process. Namely, the Heston (1993) closed-form solution model and the Hull and White (1988) model in a series expansion form, both allowing for arbitrary correlation between increments. The empirical study is carried out on French PXL European call options written on the CAC 40 index during the first half of year 2001. This paper fulfills the lack of option pricing empirical studies devoted to the French market. We discuss calibration of the models and results obtained from the out-of-sample pricing using analysis in cross-section. We also discuss the empirical dynamic of the skew. We found that misprising was globally deacreasing with maturity and increasing with low strike prices. We find that the Heston (1993) model was more likely to capture the changes in the implied volatility regime in that it can allows smile patterns to transform into skew patterns while the Hull and White (1988) model allows only for changes in the skew slope sign. We explain to what extent this phenomenon is linked with the values of some of the structural parameters.

Implied Volatility, Stochastic Volatility Model, Skew and Smile

Abstract:
This paper is the first illustrated review of literature on local and implied volatility. It presents and discusses both concepts that are central in risk management. If local volatility is a relatively recent concept, implied volatility has emerged in the 70's as a global measure of uncertainty in the economy, typically used to calibrate option theoretical prices to market prices. Local volatilities has appeared in the mid 90's as a forward or instantaneous measure of volatility. This work displays the feature of each volatility model and highlights the role of all the structural parameters that drive the volatility process.

Implied Volatility, Local Volatility, Stochastic Volatility, GARCH Volatility, Smile, Skew

Abstract:
Asymmetric volatility in equity markets has been widely documented in finance, where two competing explanations, as considered in Bekaert and Wu (2000), are the financial leverage and the volatility feedback hypothesis. We explicitly test for the role of both hypotheses in explaining extreme daily U.S. equity market movements during the period January 1990 to September 2008. To this aim, we examine asymmetric volatility based on a novel model of market returns, conditional market volatility and volatility of volatility. We then test for extreme asymmetry and the distinct predictions of both hypotheses. Our results document significant extreme asymmetric volatility. This effect is contemporaneous, consistent with both hypotheses, and it is important for large market declines. We further point out aggregate asset pricing implications under extreme volatility feedback.

market volatility, asymmetric volatility, leverage effect, volatility feedback, VIX, market stress

Abstract:
This article analyses, for the first time, the financial impact on the French market of September 11th, 2001. Was there any information asymmetry around this date? How deep was the reaction of the French investors? This study measures the magnitude of the shock in the stock price process.

Information costs, implied volatility, jump diffusion model

Abstract:
Oil price behavior has been a central interest throughout the economics literature due to its major impact on the world global economy for many years. The main characteristic of this strategic resource is that its price and volatility has been driven by all the major political and economical events. This has leaded the hydrocarbon market to be deeply affected by volatility transmission through correlation channel. A little attention had been devoted to the effect of the 9/11 on the behavior of crude oil prices. This article brings a special focus on the dynamic correlation structure between the two major oil markets - the US and UK oil markets - surrounding September 11th, 2001. Our results may be summarizing as follows. First, although volatility fluctuates strongly, shocks to volatility are short-lived, about 8 trading days. Indeed, persistence of volatility in Brent and West Texas Intermediate (hereafter WTI) crude oil prices is quite transitory. Second, we observe high correlation levels in response to OPEC decisions. Finally, the September 9/11 has a very short effect on the crude oil prices volatility.

C32, F3, Q40