Related papers: Path-dependent option pricing with two-dimensional…
Pricing multi-asset options via the Black-Scholes PDE is limited by the curse of dimensionality: classical full-grid solvers scale exponentially in the number of underlyings and are effectively restricted to three assets. Practitioners…
In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for…
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…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice…
We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular…
Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods…
We explore credit risk pricing by modeling equity as a call option and debt as the difference between the firm's asset value and a put option, following the structural framework of the Merton model. Our approach proceeds in two stages:…
Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume…
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…
We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and…
The concept of the path-dependent partial differential equation (PPDE) was first introduced in the context of path-dependent derivatives in financial markets. Its semilinear form was later identified as a non-Markovian backward stochastic…
Port-Hamiltonian systems (PHS) and interconnection and damping assignment passivity-based control (IDA-PBC) have achieved broad success in modelling and stabilisation of physical systems. However, the absence of a dedicated scalar potential…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
This study develops a numerical scheme for path-dependent FBSDEs and PDEs. We introduce a Picard iteration method for solving path-dependent FBSDEs, prove its convergence to the true solution, and establish its rate of convergence. A key…
In this paper we analyze a nonlinear Black--Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price $V$ is assumed to be a function of the underlying…
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent…
This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same…
In this paper, we deal with numerical approximations for solving the Black-Scholes Partial Differential Equation (PDE). This PDE is well known to be degenerated. The space discretization is performed using the classical finite volume method…
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…