The jump component of S&P 500 volatility and the VIX index

Much research has investigated the differences between option implied volatilities and econometric model-based forecasts. Implied volatility is a market determined forecast, in contrast to model-based forecasts that employ some degree of smoothing of past volatility to generate forecasts. Implied volatility has the potential to reflect information that a model-based forecast could not. This paper considers two issues relating to the informational content of the S&P 500 VIX implied volatility index. First, whether it subsumes information on how historical jump activity contributed to the price volatility, followed by whether the VIX reflects any incremental information pertaining to future jump activity relative to model-based forecasts. It is found that the VIX index both subsumes information relating to past jump contributions to total volatility and reflects incremental information pertaining to future jump activity. This issue has not been examined previously and expands our understanding of how option markets form their volatility forecasts.

Exploiting the cointrgration between vix and CDS in a credit market timing model

We investigate the cointegration between VIX and CDS indices, and the possibility of exploiting it in an existing credit market timing investment model. We find cointegration over most of the sample period and the leadership of VIX over the CDS in the price discovery process. We present two methods for including cointegration into the model. Both strategies improve the in-sample and out-of-sample model performances, even though out-of-sample results are weaker. We find that in-sample better performances are explained by a stronger cointegration, concluding that in the presence of cointegration our strategies can be profitable in an investment model that considers transaction costs.

ViX : una aplicación informática abierta para la visualización y estudio interactivo de la anatomía en 3D.

Monográfico con el título: 'Avances tecnológicos digitales en metodologías de innovación docente en el campo de las Ciencias de la Salud en España'. Resumen basado en el de la publicación

Testando o poder preditivo do VIX: uma aplicação do modelo de erro multiplicativo

O VIX Volatility Index surgiu como uma alternativa no cálculo da volatilidade implícita, visando mitigar alguns problemas encontrados em modelos da família Black-Scholes. Este tipo de volatilidade é tida como a melhor previsora da volatilidade futura, dado que as expectativas dos operadores de opções se encontram embutidas em seus valores. O objetivo deste trabalho é testar se o VIX apresenta maior poder preditivo e informações relevantes não presentes em modelos de séries temporais para variáveis não-negativas, tratadas através do modelo de erro multiplicativo. Os resultados indicam que o VIX apresenta maior poder preditivo em períodos de estabilidade econômica, mas não contém informação relevante frente à real volatilidade. Em períodos de crise econômica o resultado se altera, com o VIX apresentando o mesmo poder explicativo, mas contém informações relevantes no curto prazo.

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Gabrielis Putherbei Turonici professione Fontebraldaei, Theotimus, sive de tollendis & expungendis malis libris, iis praecipue, quos vix incolumi fide ac pietate plerique legere queant, libri tres, multa complectentes, quae tum ad mores, tum ad religionem faciant, & lectorem oppido iuuent, cuiuscunque tandem fidei illum nacti erunt

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Financialization, crisis and commodity correlation dynamics

Stronger investor interest in commodities may create closer integration with conventional asset markets. We estimate sudden and gradual changes in correlation between stocks, bonds and commodity futures returns driven by observable financial variables and time, using double smooth transition conditional correlation (DSTCC–GARCH) models. Most correlations begin the 1990s near zero but closer integration emerges around the early 2000s and reaches peaks during the recent crisis. Diversification benefits to investors across equity, bond and stock markets were significantly reduced. Increases in VIX and financial traders’ short open interest raise futures returns volatility for many commodities. Higher VIX also increases commodity returns correlation with equity returns for about half the pairs, indicating closer integration.

Modeling and Forecasting Implied Volatility: Implications for Trading, Pricing, and Risk Management

Modeling and forecasting of implied volatility (IV) is important to both practitioners and academics, especially in trading, pricing, hedging, and risk management activities, all of which require an accurate volatility. However, it has become challenging since the 1987 stock market crash, as implied volatilities (IVs) recovered from stock index options present two patterns: volatility smirk(skew) and volatility term-structure, if the two are examined at the same time, presents a rich implied volatility surface (IVS). This implies that the assumptions behind the Black-Scholes (1973) model do not hold empirically, as asset prices are mostly influenced by many underlying risk factors. This thesis, consists of four essays, is modeling and forecasting implied volatility in the presence of options markets’ empirical regularities. The first essay is modeling the dynamics IVS, it extends the Dumas, Fleming and Whaley (DFW) (1998) framework; for instance, using moneyness in the implied forward price and OTM put-call options on the FTSE100 index, a nonlinear optimization is used to estimate different models and thereby produce rich, smooth IVSs. Here, the constant-volatility model fails to explain the variations in the rich IVS. Next, it is found that three factors can explain about 69-88% of the variance in the IVS. Of this, on average, 56% is explained by the level factor, 15% by the term-structure factor, and the additional 7% by the jump-fear factor. The second essay proposes a quantile regression model for modeling contemporaneous asymmetric return-volatility relationship, which is the generalization of Hibbert et al. (2008) model. The results show strong negative asymmetric return-volatility relationship at various quantiles of IV distributions, it is monotonically increasing when moving from the median quantile to the uppermost quantile (i.e., 95%); therefore, OLS underestimates this relationship at upper quantiles. Additionally, the asymmetric relationship is more pronounced with the smirk (skew) adjusted volatility index measure in comparison to the old volatility index measure. Nonetheless, the volatility indices are ranked in terms of asymmetric volatility as follows: VIX, VSTOXX, VDAX, and VXN. The third essay examines the information content of the new-VDAX volatility index to forecast daily Value-at-Risk (VaR) estimates and compares its VaR forecasts with the forecasts of the Filtered Historical Simulation and RiskMetrics. All daily VaR models are then backtested from 1992-2009 using unconditional, independence, conditional coverage, and quadratic-score tests. It is found that the VDAX subsumes almost all information required for the volatility of daily VaR forecasts for a portfolio of the DAX30 index; implied-VaR models outperform all other VaR models. The fourth essay models the risk factors driving the swaption IVs. It is found that three factors can explain 94-97% of the variation in each of the EUR, USD, and GBP swaption IVs. There are significant linkages across factors, and bi-directional causality is at work between the factors implied by EUR and USD swaption IVs. Furthermore, the factors implied by EUR and USD IVs respond to each others’ shocks; however, surprisingly, GBP does not affect them. Second, the string market model calibration results show it can efficiently reproduce (or forecast) the volatility surface for each of the swaptions markets.

Essays on Applications of the Factor Model

Thesis (Ph.D.)--University of Washington, 2013

Nonparametric estimation of the leverage effect: a trade-off between robustness and efficiency

We consider two new approaches to nonparametric estimation of the leverage effect. The first approach uses stock prices alone. The second approach uses the data on stock prices as well as a certain volatility instrument, such as the CBOE volatility index (VIX) or the Black-Scholes implied volatility. The theoretical justification for the instrument-based estimator relies on a certain invariance property, which can be exploited when high frequency data is available. The price-only estimator is more robust since it is valid under weaker assumptions. However, in the presence of a valid volatility instrument, the price-only estimator is inefficient as the instrument-based estimator has a faster rate of convergence. We consider two empirical applications, in which we study the relationship between the leverage effect and the debt-to-equity ratio, credit risk, and illiquidity.

A simplified pricing model for volatility futures

We develop a general model to price VIX futures contracts. The model is adapted to test both the constant elasticity of variance (CEV) and the Cox–Ingersoll–Ross formulations, with and without jumps. Empirical tests on VIX futures prices provide out-of-sample estimates within 2% of the actual futures price for almost all futures maturities. We show that although jumps are present in the data, the models with jumps do not typically outperform the others; in particular, we demonstrate the important benefits of the CEV feature in pricing futures contracts. We conclude by examining errors in the model relative to the VIX characteristics