Related papers: A First Option Calibration of the GARCH Diffusion …

This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation…

In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…

Here, we have analysed a GARCH(1,1) model with the aim to fit higher order moments for different companies' stock prices. When we assume a gaussian conditional distribution, we fail to capture any empirical data when fitting the first three…

We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as…

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…

Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…

We propose a novel Black-Scholes model under which the stock price processes are modeled by stochastic differential equations driven by sub-diffusions. The new framework can capture the less financial activity phenomenon during the bear…

Gasoline blending scheduling uses resource allocation and operation sequencing to meet a refinery's production requirements. The presence of nonlinearity, integer constraints, and a large number of decision variables adds complexity to this…

This paper introduces a unified approach for modeling high-frequency financial data that can accommodate both the continuous-time jump-diffusion and discrete-time realized GARCH model by embedding the discrete realized GARCH structure in…

We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order $-\alpha$ with $-1<\alpha<0$. For exact time-marching, we derive optimal algebraic error estimates…

A linear semi-implicit hybridizable discontinuous Galerkin (HDG) scheme is proposed to solve the diffusive Peterlin viscoelastic model, allowing the diffusion coefficient $\ep$ of the conformation tensor to be arbitrarily small. We…

American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods…

The single-step one-shot method has proven to be very efficient for PDE-constrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization…

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a simplified semilinear gradient enhanced damage model. The model equations are of a special structure as the state equation…

In this paper we present a simple, but new, approximation methodology for pricing a call option in a Black \& Scholes market characterized by stochastic interest rates. The method, based on a straightforward Gaussian moment matching…

In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…

Diffusion models have proven to be highly effective in image and video generation; however, they encounter challenges in the correct composition of objects when generating images of varying sizes due to single-scale training data. Adapting…

In this paper, we introduce a new finite expression method (FEX) to solve high-dimensional partial integro-differential equations (PIDEs). This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel…

In this paper, the valuation of European and path-dependent options in foreign exchange (FX) markets is considered when the currency exchange rate evolves according to the Heston model combined with the Cox-Ingersoll-Ross dynamics for the…

Diffusion models are state-of-the-art generative models, yet their samples often fail to satisfy application objectives such as safety constraints or domain-specific validity. Existing techniques for alignment require gradients, internal…