相关论文: Reduced basis methods for pricing options with the…

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…

We derive a recursive formula for arithmetic Asian option prices with finite observation times in semimartingale models. The method is based on the relationship between the risk-neutral expectation of the quadratic variation of the return…

We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise…

A unified analytical pricing framework with involvement of the shot noise random process has been introduced and elaborated. Two exactly solvable new models have been developed. The first model has been designed to value options. It is…

We provide an European option pricing formula written in the form of an infinite series of Black Scholes type terms under double Levy jumps model, where both the interest rate and underlying price are driven by Levy process. The series…

We compare the option pricing formulas of Louis Bachelier and Black-Merton-Scholes and observe -- theoretically as well as for Bachelier's original data -- that the prices coincide very well. We illustrate Louis Bachelier's efforts to…

This paper presents the Runge-Kutta-Legendre finite difference scheme, allowing for an additional shift in its polynomial representation. A short presentation of the stability region, comparatively to the Runge-Kutta-Chebyshev scheme…

Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of…

In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional…

In the present work, the European option pricing SWIFT method is extended for Heston model calibration. The computation of the option price gradient is simplified thanks to the knowledge of the characteristic function in closed form. The…

In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option…

We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample…

In this paper an improved Cuckoo Search Algorithm is developed to allow for an efficient and robust calibration of the Heston option pricing model for American options. Calibration of stochastic volatility models like the Heston is…

In this paper, we consider option pricing in a framework of the fractional Heston-type model with $H>1/2$. As it is impossible to obtain an explicit formula for the expectation $\mathbb E f(S_T)$ in this case, where $S_T$ is the asset price…

We derive error estimates for multinomial approximations of American options in a multidimensional jump--diffusion Merton's model. We assume that the payoffs are Markovian and satisfy Lipschitz type conditions. Error estimates for such type…

This paper deals with the numerical solution of the Heston partial differential equation that plays an important role in financial option pricing, Heston (1993, Rev. Finan. Stud. 6). A feature of this time-dependent, two-dimensional…

In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes…

In this paper, an integral equation representation for the early exercise boundary of an American option contract is considered. Thus far, a number of different techniques have been proposed in the literature to obtain a variety of integral…

Here we develop an option pricing method based on Legendre series expansion of the density function. The key insight, relying on the close relation of the characteristic function with the series coefficients, allows to recover the density…

In this contribution we are concerned with tight a posteriori error estimation for projection based model order reduction of $\inf$-$\sup$ stable parameterized variational problems. In particular, we consider the Reduced Basis Method in a…