Related papers: Decomposition formula for rough Volterra stochasti…
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a…
We present a novel Monte Carlo based LSV calibration algorithm that applies to all stochastic volatility models, including the non-Markovian rough volatility family. Our framework overcomes the limitations of the particle method proposed by…
It has been recently shown that spot volatilities can be very well modeled by rough stochastic volatility type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than 1/2. This…
In general, the pricing of variable annuities with guarantees can be done by solving the corresponding optimal stochastic control problem if the contract withdrawal strategy is assumed to be optimal. This is typically solved as a dynamic…
We solve a family of fractional Riccati differential equations with constant (possibly complex) coefficients. These equations arise, e.g., in fractional Heston stochastic volatility models, that have received great attention in the recent…
We propose a quasi maximum likelihood estimation method for Bergomi-type stochastic volatility models with parametrized kernels, focusing on the estimation of the kernel parameters from high-frequency time-series observations of option…
This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent…
Fourier-based methods are central to option pricing and hedging when the Fourier-Laplace transform of the log-price and integrated variance is available semi-explicitly. This is the case for the Volterra Stein-Stein stochastic volatility…
This paper proposes the sample path generation method for the stochastic volatility version of CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model…
In this study, we propose a new formula for spread option pricing with the dependence of two assets described by a copula function. The advantage of the proposed method is that it requires only the numerical evaluation of a one-dimensional…
This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices…
The quadratic rough Heston model provides a natural way to encode Zumbach effect in the rough volatility paradigm. We apply multi-factor approximation and use deep learning methods to build an efficient calibration procedure for this model.…
Existing deep learning-based calibration scheme for rough volatility models predominantly rely on supervised learning frameworks, which incur significant computational costs due to the necessity of generating massive synthetic training…
In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model, by using an asymptotic approach. To find the explicit…
This study presents contemporaneous modeling of asset return and price range within the framework of stochastic volatility with leverage. A new representation of the probability density function for the price range is provided, and its…
This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented…
We provide a simple method to estimate the parameters of multivariate stochastic volatility models with latent factor structures. These models are very useful as they alleviate the standard curse of dimensionality, allowing the number of…
We propose a parameter-free model for estimating the price or valuation of financial derivatives like options, forwards and futures using non-supervised learning networks and Monte Carlo. Although some arbitrage-based pricing formula…
We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go…
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…