quantfinanceclub.com

Implied Probability Measures of Volatility

We explore the inversion of derivatives prices to obtain an implied probability measure on volatility’s hidden state. Stochastic volatility is a hidden Markov model (HMM), and HMMs ordinarily warrant filtering. However, derivative data is a set of conditional expectations that are already observed in the market, so rather than use filtering techniques we compute an \textit{implied distribution} by inverting the market’s option prices. Robustness is an issue when model parameters are probably unknown, but isn’t crippling in practical settings because the data is sufficiently imprecise and prevents us from reducing the fitting error down to levels where parameter uncertainty will show. When applied to SPX data, the estimated model and implied distributions produce variance swap rates that are consistent with the VIX, and also pick up some of the monthly effects that occur from option expiration. We find that parsimony of the Heston model is beneficial because we are able to decipher behavior in estimated parameters and implied measures, whereas the richer Heston model with jumps produces a better fit but also has implied behavior that is less revealing.

Link al Paper

(Fuente: Global Weekly Snapshot, Fixed Income & Economic Research, Credit Suisse, 10 February 2012)

Explosive Volatility: A Model of Financial Contagion

This paper proposes a model of financial contagion that accounts for explosive, mutually exciting shocks to market volatility. We fit the model using country-level data during the European sovereign debt crisis, which has its roots in the period 2008–2010, and was continuing to affect global markets as of October, 2011. Our analysis shows that existing volatility models are unable to explain two key stylized features of global markets during presumptive contagion periods: shocks to aggregate market volatility can be sudden and explosive, and they are associated with specific directional biases in the cross-section of country-level returns. Our model repairs this deficit by assuming that the random shocks to volatility are heavy-tailed and correlated cross-sectionally, both with each other and with returns.
We find evidence for significant contagion effects during the major EU crisis periods of May 2010 and August 2011, where contagion is defined as excess correlation in the residuals from a factor model incorporating global and regional market risk factors. Some of this excess correlation can be explained by quantifying the impact of shocks to aggregate volatility in the cross-section of expected returns—but only, it turns out, if one is extremely careful in accounting for the explosive nature of these shocks. We show that global markets have time-varying cross-sectional sensitivities to these shocks, and that high sensitivities strongly predict periods of financial crisis. Moreover, the pattern of temporal changes in correlation structure between volatility and returns is readily interpretable in terms of the major events of the periods in question.

Link al Paper

(Fuente: Yahoo Finance)

The Implied Volatility of ETF and Index Options

Abstract: 
We examine the option-implied volatility of the three most liquid ETFs (Diamonds, Spiders, and Cubes) and their respective tracking indices (Dow 30, S&P 500, and NASDAQ 100). We find that volatility smiles for ETF options are more pronounced than for index options, primarily because deep-in-themoney ETF options have considerably higher implied volatility than deep-in-the-money index options. The observed difference in implied volatility is not due to a difference between the realized return distributions of the underlying ETFs and indices. Differences in implied volatility for ETF and index options also do not appear to be explained by discrepancies in net buying pressure, as theorized by Bollen and Whaley (2004).

Link al Paper

Debido al aumento de volatilidad en el Forex, un concepto interesante para aprender es el Risk Reversal.

(…) This indicator represents a proxy for investor concerns that (currency) will collapse suddenly, and its high level suggests that this is indeed a growing concern. (…)

Según Investopedia

In foreign-exchange trading, risk reversal is the difference in volatility (delta) between similar call and put options, which conveys market information used to make trading decisions.

Para Sala de Inversiones

Muestra la diferencia en volatilidad, y por tanto en precio, entre las puts y las calls sobre las opciones out of the money más liquidas cotizadas en el mercado al contado. Los valores positivos indican que las calls son más caras que las puts (la protección al alza en el subyacente spot es relativamente más cara), mientras que los valores negativos indican que las puts son más caras que las calls (la protección a la baja en el subjacente spot es más cara). Los cambios significativos pueden indicar un cambio en las expectativas de mercado para la dirección futura del tipo de cambio de divisas subyacente spot.

Conforme a Global Market Financial Institute,

The market has established a 25 (0.25) delta benchmark for risk reversal quotes.

Listo con las definiciones básicas, ahora el DB tiene una muy buena guía-del 2006- para sacarle provecho al tema.