investing in stock markets usually is involved in more risks than the bounds and bank deposits. it is expected that resulting returns (capital gain plus yields) from trading in a stock market to be more than those of in a risk free investment. therefore, developing accurate techniques of estimation and forecasting in volatility analysis of financial markets is inevitable. sum squares of weekly ...

We show that the information in European option prices reveals, robustly and nonparametrically, the no-arbitrage prices of general volatility derivatives – contracts on the realized variance of an underlying price process. Our explicit formulas are exact and valid across all dynamics satisfying an independence assumption on the instantaneous volatility. Our methods are moreover immunized, to fi...

We use high-frequency data to study the dynamic relationship between volatility and equity returns. We provide evidence on two alternative mechanisms of interaction between returns and volatilities: the leverage effect and the volatility feedback effect. The leverage hypothesis asserts that return shocks lead to changes in conditional volatility, while the volatility feedback effect theory assu...

In this paper, we provide evidence on two alternative mechanisms of interaction between returns and volatilities: the leverage effect and the volatility feedback effect. We stress the importance of distinguishing between realized volatility and implied volatility, and find that implied volatilities are essential for assessing the volatility feedback effect. The leverage hypothesis asserts that ...

A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In this paper, we propose a new long memory asymmetric volatility model which captures more flexible asymmetric patterns as compared with existing models. We extend the new specification to realized volatility by taking account of measurement errors, and use the Efficient Importan...

The unbiasedness tests of implied volatility as a forecast of future realized volatility have found implied volatility to be a biased predictor. We explain this puzzle by recognizing that option prices contain a market risk premium not only on the asset itself, but also on its volatility. We show using a stochastic volatility model, that a call option price can be represented as an expected val...

Timer options are barrier style options in the volatility space. A typical timer option is similar to its European vanilla counterpart, except with uncertain expiration date. The finite-maturity timer option expires either when the accumulated realized variance of the underlying asset has reached a pre-specified level or on the mandated expiration date, whichever comes earlier. The challenge in...