S&P 500 implied volatility and monetary policy announcements

While many studies have investigated the link between macroeconomic events and equity market volatility, few have considered the impact on option implied volatilities. Given the recent focus on trading in implied volatility, in the context of the S&P 500 VIX index, this paper examines how the VIX index behaves around US monetary policy announcements. It is revealed that the VIX index falls significantly on the day of Federal Open Market Committee meetings.     

INDIFFERENCE PRICES AND IMPLIED VOLATILITIES

We consider a general local‐stochastic volatility model and an investor with exponential utility. For a European‐style contingent claim, whose payoff may depend on either a traded or nontraded asset, we derive an explicit approximation for both the buyer's and seller's indifference prices. For European calls on a traded asset, we translate indifference prices into an explicit approximation of the buyer's and seller's implied volatility surfaces. For European claims on a nontraded asset, we establish rigorous error bounds for the indifference price approximation. Finally, we implement our indifference price and implied volatility approximations in two examples.     

Modelling return and conditional volatility exposures in global stock markets

This article empirically investigates the exposure of country-level conditional stock return volatilities to conditional global stock return volatility. It provides evidence that conditional stock market return volatilities have a contemporaneous association with global return volatilities. While all the countries included in the study exhibited a significant and positive relationship to global volatility, emerging market volatility exposures were considerably higher than developed market exposures. JEL Classification G12     

Economic uncertainty,trading activity,and commodity futures volatility

This paper investigates the dynamics of commodity futures volatility. I derive the variance decomposition for the futures basis and show unexpected excess returns result from new information about expected future interest rates, convenience yields, and risk premia. Measures of uncertainty in economic conditions have significant predictive power for realized volatility of commodity futures returns, after controlling for lagged volatility, returns, commodity index trading, hedging pressure, and other trading activity, even during the so-called “index financialization” period. During this period, hedge fund performance predicts volatility in grain commodities, which are affected by the US ethanol mandate.     

How do US options traders “smirk” on China? Evidence from FXI options

In this paper, we study the implied volatility smirk (IVS) of options written on the FXI, the Financial Times Stock Exchange/Xinhua China 50 Index exchange-traded fund (ETF). Using the methodology of Zhang and Xiang (2008, Quant Financ, 8, pp. 263–284), we document the empirical characteristics of the level, slope, and curvature of IVS of the FXI options. We find that, on average, IVS becomes steeper and more convex as time to maturity increases. The level and curvature are usually positive, and the slope is negative. We provide evidence that the information in the quantified IV factors has some predictive power for the future monthly FXI ETF returns.     

Volatility of volatility is (also) rough

Using high-frequency data for major volatility indexes, we compute the volatility of volatility and show that its logarithm follows a fractional Brownian motion with Hurst parameter smaller than 1/2 thereby extending to the volatility asset class the recent findings obtained for the equity index markets. The results confirm that the volatility of volatility is a rough process and it possesses the long memory property. We also show that the correlation between the volatility and the volatility of volatility is positive, consistent with observations in the volatility option market. Lastly, a robustness check using volatility futures confirms the findings.     

Semistatic hedging and pricing American floating strike lookback options

We price an American floating strike lookback option under the Black–Scholes model with a hypothetic static hedging portfolio (HSHP) composed of nontradable European options. Our approach is more efficient than the tree methods because recalculating the option prices is much quicker. Applying put–call duality to an HSHP yields a tradable semistatic hedging portfolio (SSHP). Numerical results indicate that an SSHP has better hedging performance than a delta-hedged portfolio. Finally, we investigate the model risk for SSHP under a stochastic volatility assumption and find that the model risk is related to the correlation between asset price and volatility.     

The characteristic function of rough Heston models

It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non‐Markovian nature of the fractional Brownian motion, they raise new issues when it comes to derivatives pricing. Using an original link between nearly unstable Hawkes processes and fractional volatility models, we compute the characteristic function of the log‐price in rough Heston models. In the classical Heston model, the characteristic function is expressed in terms of the solution of a Riccati equation. Here, we show that rough Heston models exhibit quite a similar structure, the Riccati equation being replaced by a fractional Riccati equation.     

A NEW LOOK AT SHORT‐TERM IMPLIED VOLATILITY IN ASSET PRICE MODELS WITH JUMPS

We analyze the behavior of the implied volatility smile for options close to expiry in the exponential Lévy class of asset price models with jumps. We introduce a new renormalization of the strike variable with the property that the implied volatility converges to a nonconstant limiting shape, which is a function of both the diffusion component of the process and the jump activity (Blumenthal–Getoor) index of the jump component. Our limiting implied volatility formula relates the jump activity of the underlying asset price process to the short‐end of the implied volatility surface and sheds new light on the difference between finite and infinite variation jumps from the viewpoint of option prices: in the latter, the wings of the limiting smile are determined by the jump activity indices of the positive and negative jumps, whereas in the former, the wings have a constant model‐independent slope. This result gives a theoretical justification for the preference of the infinite variation Lévy models over the finite variation ones in the calibration based on short‐maturity option prices.     

VALUATION OF BARRIER OPTIONS VIA A GENERAL SELF‐DUALITY

Classical put–call symmetry relates the price of puts and calls under a suitable dual market transform. One well‐known application is the semistatic hedging of path‐dependent barrier options with European options. This, however, in its classical form requires the price process to observe rather stringent and unrealistic symmetry properties. In this paper, we develop a general self‐duality theorem to develop valuation schemes for barrier options in stochastic volatility models with correlation.