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 …

-affine volatility dynamics. We use extensive empirical data sets to study how infinite-activity Variance Gamma and Normal Inverse … Gaussian jumps with affine and non-affine volatility dynamics improve goodness of fit and option pricing performance. With …

spot volatilities from the series of VIX rather than by linking spot volatility with different dates by using the series of …

-dependent volatility as the limit of a discrete-time GARCH model. In particular, the continuous-time model is the limit of a discrete …-time GARCH model of Heston and Nandi (1997) that allows asymmetry between returns and volatility. For the continuous-time model …

Market analysts and central banks often use the implied volatility of FX options as an indicator of expected exchange … deviate the value of implied volatility from the exchange rate variability expected by the market. These biasing factors are … one month. However, implied volatility provides a biased estimate, and does not encompass the information included in …

estimates of the long-term volatility. By providing an external validation of the model using an option-based index reported by …

We consider a semi-Markov modulated market consisting of a riskless asset or bond, B, and a risky asset or stock, S …) and volatility (Theorem 2) swaps for stochastic volatilities driven by the semi-Markov processes. We also discuss some … extensions of the obtained results such as local semi-Markov volatility, Dupire formula for the local semi-Markov volatility and …

We introduce an asymptotic expansion for forward start options in a multi-factor local-stochastic volatility model. We … derive explicit approximation formulas for the so-called forward implied volatility which can be useful to price complex path … generalized to a wider class of local-stochastic volatility models. We illustrate the effectiveness of the technique through some …

models with time varying volatility. In this paper we consider models of this class and examine their potential when it comes …