In the past years, there has been an extensive investigation of the class of stochastic volatility models for the …-Scholes economy and accounting for discrepancies between observation and predictions in the simple log-normal, constant-volatility … model. In this paper, we study the structure of an options market with a stochastic volatility that will eventually vanish …

We present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which … accuracy of our method. In order to allow for the treatment of realistic inputs that may contain arbitrage, we reformulate the … input prices and the arbitrage-free prices generated by our method. To further stabilize the method in the presence of noisy …

In this paper, we introduce a 3D finite dimensional Gaussian process (GP) regression approach for learning arbitrage … is proven to be arbitrage-free along the strike direction (butterfly and call-spread arbitrages are precluded on the … entire 3D input domain). The cube is free from static arbitrage along the tenor and maturity directions if swaption prices …

were introduced to capture complex phenomena such as volatility clustering or long memory. After recalling recent results …. We also provide some tools for volatility modelling and delta hedging, as well as comparisons with numerical Fourier …

extension to stochastic volatility, while using option data for Apple (AAPL) and Google (GOOG). We find that recalibrating a …

options prices under Heston's stochastic volatility (SV) model. We demonstrate that under a particular reparametrization, this … volatility 'smile', which indicates a likely distortion in the Black-Scholes modeling of such option data. Reflective of entirely … different market expectations, this distortion in the volatility 'smile' appears not to exist in the TLT option data. We provide …

-constant volatility onto a numerical tree scheme, to evaluate a real option, using a quadrinomial multiplicative recombination. Design …/methodology/approach - This article uses the multiplicative quadrinomial tree numerical method with non-constant volatility, based on stochastic … differential equations of the GARCH-diffusion type to value real options when the volatility is stochastic. Findings - Findings …

This paper proposes the sample path generation method for the stochastic volatility version of the CGMY process. We …

Barndorff-Nielsen and Shephard (2001) proposed a class of stochastic volatility models in which the volatility follows …’s stochastic volatility models. …