We examine local-stochastic volatility models and derive a simple condition such models need to obey so that the carry …-even levels of the local volatility model - itself in the admissible class …

We consider implied volatility, time-dependent volatility, local volatility and stochastic volatility. We derive …

nonlinearity and asymmetry in the drift, and incorporates the level effect and stochastic volatility in the diffusion function is … asymmetric drift of the short rate, and the presence of nonlinearity, GARCH, and level effects in its volatility. The empirical … volatility of interest rate changes …

wide variety of stocks, bonds and options. Evidence suggests that both the expected return and the volatility vary over … considerable effort has been devoted to the modelling of time-varying volatility. Recent attention has moved to examining the … daily stock market volatility in a sample of significant emerging stock markets using an Asymetric Volatility Model (ASV …

The paper examines the relative performance of Stochastic Volatility (SV) and GARCH(1,1) models fitted to twenty plus … years of daily data for three indices. As a benchmark, I use the realized volatility (RV) for the S&P 500, DOW JONES and … volatility models, if the simple expedient of using lagged squared demeaned daily returns provides a better RV predictor, at …

We develop a discrete-time affine stochastic volatility model with time-varying conditional skewness (SVS). Importantly …, we disentangle the dynamics of conditional volatility and conditional skewness in a coherent way. Our approach allows … autoregressive conditional heteroskedasticity (GARCH), and stochastic volatility with jumps (SVJ) models. Our results are not due to …

multivariate t. This result is then applied to models of conditionally random volatility and used to derive exact results for the …

along with the specification of (a) the initial density, and (b) the volatility structure of the density. The volatility …