Volatility is an important variable in the
financial market. We propose a model-free implied volatility method to measure
the volatility and test the volatility risk premium. The model-free implied
volatility does not depend on the option pricing model, and extracts
information from all the option contracts. We provide empirical evidence from
the S & P 500 index option that model-free implied volatility is more
accurate to forecast the future volatility and the volatility risk premium does
not exist.

Abstract:
Due to the unobserved nature of the true return
variation process, one of the most challenging problems in evaluation of
volatility forecasts is to find an accurate benchmark proxy for ex-post volatility. This paper uses the Australian equity market ultra-high-frequency
data to construct an unbiased ex-post volatility estimator and then use
it as a benchmark to evaluate various practical volatility forecasting
strategies (GARCH class model based). These forecasting strategies allow for
the skewed distribution of innovations and use various estimation windows in
addition to the standard GARCH volatility models. In out-of-sample tests, we
find that forecasting errors across all model specifications are systematically
reduced if using the unbiased ex-post volatility estimator compared with
those using the realized volatility based on sparsely sampled intra-day data.
In particular, we show that the three benchmark forecasting models outperform
most of the modified strategies with different distribution of returns and
estimation windows. Comparing the three standard GARCH class models, we find
that the asymmetric power ARCH (APARCH) model exhibits the best forecasting
power in both normal and financial turmoil periods, which indicates the ability
of APARCH model to capture the leptokurtic returns and stylized features of
volatility in the Australian stock market.

Abstract:
The paper analyses how volatility derivatives on the volatility index VIX can be used as trading and risk management tools for investors and trad-ers. Volatility and the different types of volatility are discussed. It elabo-rates upon assumptions of option pricing models and specifies which complications accompany the determination of volatility. The weaknesses of the Black-Scholes-Merton model are illuminated and the difference between the model assumptions regarding volatility and market reality is identified. Using the skew- and term-curve-effect, the paper demonstrates how volatility behaves in reality towards other model parameters. In terms of pure volatility trading, the volatility derivatives are presented and analysed in terms of their merits and fields of application. Additionally, the stylized facts about volatility are considered. The paper shows how VIX futures and options can hedge equity portfolios and when they are superior to traditional hedging alternatives and compares the outcome of a VIX hedging strategy with a Buy & Hold strategy of the S & P 500 index over a time period of 20 years.

Abstract:
The present study attempts to track the transmission
of volatility across major international stock markets over a span of 20 years, which includes
both crisis (contagion form) and non-crisis periods.
It also investigates whether global transmission of volatility follows a
pattern. The study uses bi-variate EGARCH model in order to capture
spillover between a pair of stock markets and the estimation window is one year
with a sliding frequency of one quarter. The results show that, there is a spillover
of volatility between international stock markets at all times. Results also indicate
that in almost all cases, the pattern of spillover is non-random. Finally, the
study characterizes the spillover pattern
between international stock markets using suitable theoretical distributions.

Abstract:
In this paper, we assess how to recover the volatility of interest rates in the euro area money market, on the sole basis of the zero-coupon yield curve. Our primary result is that there exists an empirical regularity (linking rates and volatility) that takes a relatively simple mathematical form. We also show that the existence of such regularity cannot be explained by a reasoning based on the hypothesis of absence of opportunities of arbitrage since a continuous-time arbitrage-free model may produce instances of curves that are consistent with a continuum of level of volatilities. We exhibit an example for this.

Abstract:
Considering the overnight effect on the stock market, we construct a daily
volatility measure that is formed by a linear combination of the three components,
namely overnight volatility, morning realized volatility and afternoon
realized volatility, and obtain the optimal solution in theory. An empirical
work is performed for studying the daily volatility structure of Shanghai
stock index and Shenzhen stock index in China’s stock market by using our
daily volatility measure. The empirical results show that, the daily volatility
measure considering the impact of overnight variance and time segment performs
better than original volatility measure.

Abstract:
The 2008 financial crisis has produced volatility levels not seen since the 1987 stock market crash more than 20 years ago. During that time, the culprit was thought to be index futures and program trading. This time, leveraged ETFs and their rebalancing trades have been singled out by some to explain both the spike in volatility and the appearance of large price swings at the end of the trading day. This study examines the merit of these accusations and whether the increase in volatility and end of the day price momentum is indeed linked to leveraged ETFs and their rebalancing trades. For the S&P 500, the relationship appears to be a spurious coincidence.

Abstract:
The reduced form solutions of indeterminate rational expectations models often include extraneous expectational errors or “sunspots”. Sunspots are usually modeled as independent of the model’s fundamentals, and are often presumed to result in excess volatility. An alternate approach, however, is to assume that sunspots include both an overreaction or underreaction to fundamentals, as well as genuine extraneous noise. This paper uses a simple linear model to formally show how the relationship between sunspots and fundamentals affects aggregate volatility. Sunspots reduce volatility if 1) they include an undereaction to fundamentals, 2) the variance of genuine extraneous noise is sufficiently small, and 3) the root that causes indeterminacy is sufficiently far from one.

Abstract:
Stochastic volatility models are used in mathematical finance to describe the dynamics of asset prices. In these models, the asset price is modeled as a stochastic process depending on time implicitly defined by a stochastic differential Equation. The volatility of the asset price itself is modeled as a stochastic process depending on time whose dynamics is described by a stochastic differential Equation. The stochastic differential Equations for the asset price and for the volatility are coupled and together with the necessary initial conditions and correlation assumptions constitute the model. Note that the stochastic volatility is not observable in the financial markets. In order to use these models, for example, to evaluate prices of derivatives on the asset or to forecast asset prices, it is necessary to calibrate them. That is, it is necessary to estimate starting from a set of data the values of the initial volatility and of the unknown parameters that appear in the asset price/volatility dynamic Equations. These data usually are observations of the asset prices and/or of the prices of derivatives on the asset at some known times. We analyze some stochastic volatility models summarizing merits and weaknesses of each of them. We point out that these models are examples of stochastic state space models and present the main techniques used to calibrate them. A calibration problem for the Heston model is solved using the maximum likelihood method. Some numerical experiments about the calibration of the Heston model involving synthetic and real data are presented.

We decompose UK market volatility into
short- and long-run components using EGARCH component model and examine the
cross-sectional prices of the two components. Our empirical results suggest
that these two components are significantly priced in the cross-section and the
negative risk premia are consistent with the existing literature. The Fama-French
three-factor model is improved by the inclusion of the two volatility
components. However, our ICAPM model using market excess return and the
decomposed volatility components as state variables compares inferiorly to the
traditional three-factor model.