Modeling and predicting the CBOE market volatility index

This paper performs a thorough statistical examination of the time-series properties of the daily market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies not only on the widespread consensus that the VIX is a barometer of the overall market sentiment as to what concerns investors' risk appetite, but also on the fact that there are many trading strategies that rely on the VIX index for hedging and speculative purposes. Preliminary analysis suggests that the VIX index displays long-range dependence. This is well in line with the strong empirical evidence in the literature supporting long memory in both options-implied and realized variances. We thus resort to both parametric and semiparametric heterogeneous autoregressive (HAR) processes for modeling and forecasting purposes. Our main ndings are as follows. First, we con rm the evidence in the literature that there is a negative relationship between the VIX index and the S&P 500 index return as well as a positive contemporaneous link with the volume of the S&P 500 index. Second, the term spread has a slightly negative long-run impact in the VIX index, when possible multicollinearity and endogeneity are controlled for. Finally, we cannot reject the linearity of the above relationships, neither in sample nor out of sample. As for the latter, we actually show that it is pretty hard to beat the pure HAR process because of the very persistent nature of the VIX index.

A Monthly Volatility Index for the US Economy

We estimate the monthly volatility of the US economy from 1968 to 2006 by extending the coincidentindex model of Stock and Watson (1991). Our volatility index, which we call VOLINX, hasfour applications. First, it sheds light on the Great Moderation. VOLINX captures the decrease in thevolatility in the mid-80s as well as the different episodes of stress over the sample period. In the 70sand early 80s the stagflation and the two oil crises marked the pace of the volatility whereas 09/11 is themost relevant shock after the moderation. Second, it helps to understand the economic indicators thatcause volatility. While the main determinant of the coincident index is industrial production, VOLINXis mainly affected by employment and income. Third, it adapts the confidence bands of the forecasts.In and out-of-sample evaluations show that the confidence bands may differ up to 50% with respect to amodel with constant variance. Last, the methodology we use permits us to estimate monthly GDP, whichhas conditional volatility that is partly explained by VOLINX. These applications can be used by policymakers for monitoring and surveillance of the stress of the economy.

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.

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.

The forecast quality of CBOE implied volatility indexes

We examine the forecast quality of Chicago Board Options Exchange (CBOE) implied volatility indexes based on the Nasdaq 100 and Standard and Poor's 100 and 500 stock indexes. We find that the forecast quality of CBOE implied volatilities for the S&P 100 (VXO) and S&P 500 (VIX) has improved since 1995. Implied volatilities for the Nasdaq 100 (VXN) appear to provide even higher quality forecasts of future volatility. We further find that attenuation biases induced by the econometric problem of errors in variables appear to have largely disappeared from CBOE volatility index data since 1995.

Essays on Applications of the Factor Model

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

Stops and bonanzas in the EU: Does being part of the Euro Area make a difference?

In this paper, we investigate whether being part of the euro area influences the conditional probability of going through a sudden stop or a bonanza of capital flows. Our sample period is from 1995 until 2014. We identify these two phenomena and we evaluate which push and pull factors help predict the conditional probability of experiencing one of them. We find that most countries had significant capital inflows until 2008 and that there were more sudden stops during the recent financial crisis than in any other moment in our sample. The factors that better help forecast the conditional probability of a sudden stop are global uncertainty (represented by the push factor “Volatility Index”), and the domestic economic activity (pull factors “GDP growth” and “consumer confidence”). An indicator of country risk (pull factor “change in credit rating”) is the most significant one for predicting bonanzas. Ultimately, we find no evidence that being part of the euro area influences the conditional probability of going through a sudden stop or a bonanza.

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.

Análise à volatilidade do mercado da arte

Um olhar breve para a história financeira internacional denota que, em períodos de crise ou até mesmo de depressão das principais economias mundiais, os investidores tendem a proteger os seus investimentos, muito para além dos usuais activos financeiros, como o caso das acções, obrigações, entre outros. A principal razão para tal é que, em termos empíricos, verifica-se que estes activos referidos apresentam uma elevada volatilidade, especialmente em momentos de grande turbulência nos mercados financeiros, em virtude da incerteza quanto ao futuro das economias mundiais. Assim sendo, a presente investigação realiza uma análise em torno da previsão de volatilidade dos activos associados a arte e, assim, pretende comparar com a volatilidade existente em torno dos índices ou mercados financeiros. Para tal, serão adoptados os modelos de heterocedasticidade condicional, com a finalidade de previsão de volatilidade marginal ou incondicional. A análise efectuada baseou-se na comparação da volatilidade marginal dos índices S&P 500 e DJ Euro Stoxx 50, representativos dos activos financeiros, face à volatilidade marginal das principais empresas (Christie´s e Sotheby´s) e do principal índice de arte (ArtPrice Global Index), representativos dos activos associados à arte. Os resultados evidenciam uma diferença significativa entre as volatilidades marginais ou incondicionais previstas, resultando numa menor volatilidade prevista incondicional dos activos de arte face aos activos financeiros.

A importância de um índice de volatilidade para o mercado brasileiro

Este trabalho objetiva analisar a importância de um índice de volatilidade implícita para o mercado brasileiro. Por ser conhecida como uma medida das expectativas futuras dos investidores, diversos estudos, principalmente na literatura estrangeira, tem consegui extrair importantes informações quanto às mudanças na volatilidade implícita com a chegada de novos dados sobre a economia. Analisando as opções de juros (IDI) e de dólar, este trabalho verifica que informações de dados macroeconômicos impactam a volatilidade. Os resultados demonstram que as expectativas quanto ao mercado de juros são impactadas por diversos dados, porém o mesmo não acontece com o mercado de dólar, a qual se demonstrou ser impactada somente por intervenções do Banco Central via colocação de swaps. Por fim, o trabalho conclui que existem varáveis não transacionáveis que explicam as variações na volatilidade implícita, mostrando que as volatilidades implícitas das opções possuem bastantes informações quanto às expectativas.

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.

Capital flows to Latin America: first quarter 2005

Includes bibliography

Capital flows to Latin America: recent developments

The external environment has deteriorated sharply as a result of the spiraling financial turmoil, and has led to a weakening in commodity prices and fears of a worldwide recession. Latin America and the Caribbean's fastest expansion in 40 years may be threatened as the global credit crunch makes financing scarce and squeezes demand for the region's commodities. This time around the region is better positioned to weather the crisis than in the past, given improvements in macroeconomic and financial policies as well as a reduced net dependency on external capital inflows. However, Latin American markets are feeling the effects of the crisis through a slowdown in capital inflows, large declines in stock price indexes, significant currency adjustments and an increase in debt spreads. Volatility has soared, with the closely watched Chicago Board Options Exchange Volatility Index moving to an all-time high of 70.33 on October 17, indicating that fear (rather than greed) has been ruling the markets.After reaching record lows in May 2007, emerging markets bond spreads are now above pre-Asian crisis levels. The JPMorgan EMBI+ Latin American composite widened by 146 basis points in the third quarter, with spreads reaching 448 basis points at the end of September. Spreads have widened sharply in recent weeks as foreign investors cut back regional exposure for the safety of U.S. Treasuries. The ongoing lack of liquidity and subsequent liquidation of assets is leading to a collapse in asset prices and a sharp widening in spreads. Daily spreads in October have risen to levels not seen since December 2002, making it much more difficult for governments that need financing to get it. Risk premiums for Latin corporates and sovereigns have risen substantially, but have remained well below U.S. junk (high-yield) bonds. Latin corporates are facing a steep rise in foreign exchange borrowing costs (although less than firms in other emerging markets), which raises concerns that refinancing risks will climb.So far, emerging markets vulnerabilities have been more focused on corporates, as sovereigns have improved public debt dynamics and countries' financing needs are under control. Market performance has been driven by the rapid deterioration of emerging markets bank and corporate market, as well as ongoing losses in emerging markets equities. From January to September 2008, the Morgan Stanley Capital International (MSCI) Latin American Index lost almost 28%, while the Emerging Markets Index lost 37% and the G-7 Index lost 24%. While in 2007 the Latin America component gained 47%, almost nine times as much as the MSCI-G7 index for developed markets, since mid-September 2008 stocks in Latin America have been doing worse than stocks in developed countries, as concerns about access to credit and the adverse impact of sharp falls in commodity prices and in local currencies contribute to increased risk aversion and to outflows of capital. Many governments in the region have used revenue from the commodity boom to pay down debt and build reserves. Now, facing a global financial crisis and the threat of recession in developed countries, the biggest question for Latin America is how long and deep this cyclical downturn will be, and how much it is going to reduce commodity prices. Prices for commodities such as soy, gold, copper and oil, which helped fund the region's boom, have fallen 28% since their July 2 high, according to the RJ/CRB Commodity Price Index. According to Morgan Stanley (in a September 29 report), should prices return to their 10-year average, Latin America's balanced budgets would quickly revert to a deficit of 4.1% of GDP. As risk aversion increases, investors are rapidly pulling out massive amounts of money, creating problems for local markets and banks. There is an ongoing shortage of dollars (as investors liquidate assets in Latin American markets), and as currencies depreciate, inflation concerns increase despite the global slowdown. In Brazil and Mexico, central banks deployed billions of dollars of reserves to stem steep currency declines, as companies in these countries, believing their local currencies would continue to strengthen against the U.S. dollar, took debts in dollars. Some companies also made bets using currency derivatives that have led to losses in the billions of dollars. Dramatic currency swings have caused heavy losses for many companies, from Mexico's cement giant Cemex SAB to the Brazilian conglomerate Grupo Votorantim. Mexico's third-largest retailer, Controladora Comercial Mexicana, declared bankruptcy recently after reporting huge losses related to exchange rate bets. As concerns about corporate exposure to dollar-denominated derivatives increases, yields on bonds issued by many of Brazil's and Mexico's leading companies have started to rise, sharply raising the cost of issuing new debt. Latin American external debt issuance came to a halt in the third quarter of 2008, totaling only US$ 690 million. The cost of obtaining loans for capital expenditures, M&A and debt refinancing is also rising substantially for Latin American corporates amid contagion from the U.S. financial crisis. According to bankers, a protracted trend of shortening tenors and widening spreads has intensified in the past few weeks, indicating that bank lending is quickly following the way of bonds and equity. Finally, money transfers from Latin American migrants are expected to decline for the first time this decade, as a result of economic downturns in the U.S. and Spain, inflation and a weaker dollar. The Mexican Central Bank announced that money transfers from Mexicans living in the U.S. dropped a record 12.2% in August. In 2008, migrants from the region will send some 1.7% less in remittances year-on-year when adjusted for inflation, according to the IADB, compounding the adverse effects of the deepening financial turmoil.

Three essays on asset pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lvy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.

Three Essays on Asset Pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lévy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.