Related papers: Compact finite difference method for pricing Europ…
In this article, a three-time levels compact scheme is proposed to solve the partial integro-differential equation governing the option prices under jump-diffusion models. In the proposed compact scheme, the second derivative approximation…
When the underlying asset displays oscillations, spikes or heavy-tailed distributions, the lognormal diffusion process (for which Black and Scholes developed their momentous option pricing formula) is inadequate: in order to overcome these…
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…
In this paper, we present a novel approach to solving the American put options pricing model by hugely relying on a front-fixing Crank-Nicolson finite difference method. Since the American put option pricing model is a widely used financial…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential…
In this research, we proposed a Mean Convection Finite Difference Method (MCFDM) for European options pricing. The Black-Scholes model, which describes the dynamics of a financial asset, was first transformed into a convection-diffusion…
This paper addresses an important gap in rigorous numerical treatments for pricing American options under correlated two-asset jump-diffusion models using the viscosity solution framework, with a particular focus on the Merton model. The…
We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a partial integro-differential equation, which is approximated…
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 this paper we propose a semi-analytic approach to pricing American options for time-dependent jump-diffusions models with exponential jumps The idea of the method is to further generalize our approach developed for pricing barrier,…
We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating…
Subdiffusion is a well established phenomenon in physics. In this paper we apply the subdiffusive dynamics to analyze financial markets. We focus on the financial aspect of time fractional diffusion model with moving boundary i.e. American…
This paper deals with the efficient numerical solution of the two-dimensional partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Merton jump-diffusion model.…
This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure…
In this paper, we present an implicit finite difference method for the numerical solution of the Black-Scholes model of American put options without dividend payments. We combine the proposed numerical method by using a front fixing…
Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or…
We study the pricing of derivative securities in financial markets modeled by a sub-mixed fractional Brownian motion with jumps (smfBm-J), a non-Markovian process that captures both long-range dependence and jump discontinuities. Under this…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…
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…
This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard…