The implied volatility of an option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space, allowing for a low dimensional factor representation of these dyn...

We propose a non-linear State Space representation to model ATM implied volatilities and to estimate the unobserved stochastic volatility for the underlying asset. We are able to estimate the average volatility risk premia and we can also address the presence of long memory in the unobserved volatility factor. We then applied our methodology to implied volatilities on currency options. These da...

This paper uses quantile regression to investigate the asymmetric return-volatility phenomenon with the newly adapted and robust implied volatility indices VIX, VXN, VDAX and VSTOXX. A particular goal is to quantify the effects of positive and negative stock index returns at various quantiles of the implied volatility distribution. As the level of the new volatility index increases during marke...

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...

Implied volatility indices are becoming increasingly popular as a measure of market uncertainty and as a vehicle for developing derivative instruments to hedge against unexpected changes in volatility. Although jumps are widely considered as a salient feature of volatility, their implications for volatility options and futures are not yet fully understood. This paper provides evidence indicatin...

Abstract: This paper presents a one factor and a two factor arbitrage-free interest rate models with parsimonious implied volatility functions. The models are empirically tested on the entire swaption surface in three currencies (U. S. dollar, Euro and Japanese yen) over a five year period. They are shown to be robust in explaining the swaption values, and the implied volatility functions are s...

Using sovereign CDS spreads and currency option data for Mexico and Brazil, we document that CDS spreads covary with both the currency option implied volatility and the slope of the implied volatility curve in moneyness. We propose a joint valuation framework, in which currency return variance and sovereign default intensity follow a bivariate diffusion with contemporaneous correlation. Estimat...

One obvious and major limitation in the classic Black-Scholes-Merton model is its assumption that the stock price follows a geometric Brownian motion with constant volatility. Even though there is no perfect way to determine the volatility of a stock, one thing we know for sure is that it varies in time in some random fashion. The implication of the constant volatility assumption leads to a log...

The volatility surface implied by option prices presents a structure that changes over time. The aim of this study is to present a framework to model the implied volatility of the FTSE options in real time, and to present a prototype application that implements this framework. We adapt the parametric models presented in Dumas et al (1998) to estimate the surfaces across moneyness instead of acr...

The Black-Scholes model assumes that the volatility is constant across strikes and maturity dates. However as we know, in the world of options, this is a very unrealistic assumption. Option prices for different maturities change drastically, and option prices for different strikes also experience significant variations. In this section we consider the numerical problem to compute the implied vo...