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We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the…

We study the pricing of European-style options written on forward contracts within function-valued infinite-dimensional affine stochastic volatility models. The dynamics of the underlying forward price curves are modeled within the…

Parametric estimation of stochastic differential equations (SDEs) has been a subject of intense studies already for several decades. The Heston model for instance is driven by two coupled SDEs and is often used in financial mathematics for…

We consider a large market model of defaultable assets in which the asset price processes are modelled as Heston-type stochastic volatility models with default upon hitting a lower boundary. We assume that both the asset prices and their…

Multivariate linear regression models often face the problem of heteroscedasticity caused by multiple explanatory variables. The weighted least squares estimation with univariate-dependent weights has limitations in constructing weight…

We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…

The Heston stochastic volatility model is arguably, the most popular stochastic volatility model used to price and risk manage exotic derivatives. In spite of this, it is not necessarily easy to calibrate to the market and obtain stable…

We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time.…

We study a two-dimensional McKean-Vlasov stochastic differential equation, whose volatility coefficient depends on the conditional distribution of the second component with respect to the first component. We prove the strong existence and…

We study nearly unstable bivariate cumulative heavy-tailed INAR($\infty$) processes and show that, under a one-factor parameterization and a suitable scaling, they converge to the rough Heston model. This yields a discrete-time…

In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining…

This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility…

This study provides a consistent and efficient pricing method for both Standard & Poor's 500 Index (SPX) options and the Chicago Board Options Exchange's Volatility Index (VIX) options under a multiscale stochastic volatility model. To…

Most of the empirical studies on stochastic volatility dynamics favor the 3/2 specification over the square-root (CIR) process in the Heston model. In the context of option pricing, the 3/2 stochastic volatility model is reported to be able…

We use modifications of the Adams method and very fast and accurate sinh-acceleration method of the Fourier inversion (iFT) (S.Boyarchenko and Levendorski\u{i}, IJTAF 2019, v.22) to evaluate prices of vanilla options; for options of…

We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clustering feature by adding…

We propose a straightforward and effective method for discretizing multi-dimensional diffusion processes as an extension of Milstein scheme. The new scheme is explicitly given and can be simulated using Gaussian variates, requiring the same…

We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in barrier options under the Heston (1993) stochastic volatility model. This is done by modifying the LT method from Imai and Tan (2006) for the Heston model such that…

The HEat modulated Infinite DImensional Heston (HEIDIH) model and its numerical approximation are introduced and analyzed. This model falls into the general framework of infinite dimensional Heston stochastic volatility models of (F.E.…

We find various exact solutions for a new stochastic volatility (SV) model: the transition probability density, European-style option values, and (when it exists) the martingale defect. This may represent the first example of an SV model…