Related papers: Compact finite difference method for pricing Europ…
Recognizing the importance of jump risk in option pricing, we propose a neural jump stochastic differential equation model in this paper, which integrates neural networks as parameter estimators in the conventional jump diffusion model. To…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
We study option prices in financial markets where the risky asset prices are modelled by jump diffusions. It was proposed by Schweizer (1996) in a general semimartingale setting, following earlier works by F\"ollmer and Sondermann (1986)…
It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the…
We propose an adaptive and explicit fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme to solve the American put options problem. First, the free boundary problem is converted into a system of partial…
This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…
We present a new approximation scheme for the price and exercise policy of American options. The scheme is based on Hermite polynomial expansions of the transition density of the underlying asset dynamics and the early exercise premium…
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We…
In this note we consider the approximation of the Greeks Delta and Gamma of American-style options through the numerical solution of time-dependent partial differential complementarity problems (PDCPs). This approach is very attractive as…
This paper deals with the numerical approximation of American-style option values governed by partial differential complementarity problems. For a variety of one- and two-asset American options we investigate by ample numerical experiments…
We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these…
In this paper, we develop novel numerical methods based on the Multi-Point Flux Approximation (MPFA) method to solve the degenerated partial differential equation (PDE) arising from pricing two-assets options. The standard MPFA is used as…
This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space…
The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes…
This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for…
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 investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we…
In this work, we analyze a Crank-Nicolson type time stepping scheme for the subdiffusion equation, which involves a Caputo fractional derivative of order $\alpha\in (0,1)$ in time. It hybridizes the backward Euler convolution quadrature…
In this paper, our focus lies on the Merton's jump diffusion model, employing jump processes characterized by the compound Poisson process. Our primary objective is to forecast the drift and volatility of the model using a variety of…
This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite…