market, volatility and jump risks, and observation error of time changes. To operationalize the models, we use volume …

The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the … process for the volatility is nonnegative and mean-reverting, which is what we observe in the markets. Secondly, there exists …. -- Heston model ; vanilla option ; stochastic volatility ; Monte Carlo simulation ; Feller condition ; option pricing with FFT …

In this paper we examine the Heston model in the limit of infinitely fast mean-reversion for the stochastic volatility … process (CIR). We show that, under an appropriate scaling of the model parameters, the two-factor stochastic volatility Heston … properties of the implied volatility surface. The model is expected to provide a reasonable fit to the market for all maturities …

We study the mass at the origin in the uncorrelated SABR stochastic volatility model, and derive several tractable … -- we derive small-strike expansions for the implied volatility when the maturity becomes short or large. These formulae, by … de finition arbitrage free, allow us to quantify the impact of the mass at zero on existing implied volatility …

implemented and do not contain any numerical integration.These formulas are important in volatility surface construction and CMS …

condition, which assigns some fixed value to the stochastic volatility subprocess, is illogical and greatly underestimates the … effect of the hidden variable. For instance, a stochastic volatility model generates a significantly weaker implied … volatility smile at short maturities. A good initial condition should specify the distribution of the hidden variable instead of …

If a high degree of accuracy and market consistency is required for option pricing, stochastic local volatility models … alternative approach using effective stochastic volatility techniques, which allow an efficient direct calibration of the leverage … function for a large class of stochastic local volatility models. This includes stochastic volatility models such as the SABR …

This paper develops a new version of the Hull-White's model of interest rates, in which the volatility of the short … constant volatility of the Brownian motion is replaced by a multifractal process so as to capture persistent volatility shocks …