Brownian motion. -- asymptotic uniformity ; local limit theorem ; volatility …

volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM), and can be tracked using … Bayesian filtering. However, derivative data can be considered as conditional expectations that are already observed in the … market, so we can input derivative prices into an inverse problem, and the solution obtained will be an implied conditional …

maturities and moneyness dimension is neglected. In this paper we propose to estimate the implied volatility surface at each … point in time nonparametrically and to analyze the implied volatility surface slice by slice with a common principal … study a p variate random vector of k groups, say the "volatility smile" at p different grid points of moneyness for k …

In this paper we examine the empirical performance of affine jump diffusion models with stochastic volatility in a time … method. The support for a stochastic volatility model including jumps in both prices and volatility is strong and the model …

Volatility long memory is a stylized fact that has been documented for a long time. Existing literature have two ways … to model volatility long memory: component volatility models and fractionally integrated volatility models. This paper … GARCH(1, 1) model by generating 37% less option pricing errors. With stronger volatility persistence, it also dominates a …

compute derivative prices. To this end, the relationship between the physical and the risk adjusted probability measure is … virtually any stochastic volatility model model can be approximated arbitrarily well by a carefully chosen continuous time … illustrates these contributions of the paper, estimating a stochastic volatility jump diffusion model …