Related papers: Fast American Option Pricing using Nonlinear Stenc…
We study perpetual American option pricing problems in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values of its maximum and maximum drawdown.…
This paper develops three polynomial-time pricing techniques for European Asian options with provably small errors, where the stock prices follow binomial trees or trees of higher-degree. The first technique is the first known Monte Carlo…
In this research, we explore neural network-based methods for pricing multidimensional American put options under the BlackScholes and Heston model, extending up to five dimensions. We focus on two approaches: the Time Deep Gradient Flow…
We present an efficient and stable numerical ansatz for solving a class of integro-differential equations. We define the class as integro-differential equations with increasingly smooth memory kernels. The resulting algorithm reduces the…
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…
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…
In this paper a time-fractional Black-Scholes model (TFBSM) is considered to study the price change of the underlying fractal transmission system. We develop and analyze a numerical method to solve the TFBSM governing European options. The…
An accurate valuation of American call options is critical in most financial decision making environments. However, traditional models like the Barone-Adesi Whaley (B-AW) and Binomial Option Pricing (BOP) methods fall short in handling the…
In this paper we provide a quantum Monte Carlo algorithm to solve multidimensional Black-Scholes PDEs with correlation for option pricing. The payoff function of the option is of general form and is only required to be continuous and…
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…
The purpose of this paper is to analyze the problem of option pricing when the short rate follows subdiffusive fractional Merton model. We incorporate the stochastic nature of the short rate in our option valuation model and derive explicit…
Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a…
This study investigates the application of machine learning algorithms, particularly in the context of pricing American options using Monte Carlo simulations. Traditional models, such as the Black-Scholes-Merton framework, often fail to…
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…
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…
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…
We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a…
We compare the CPU effort and pricing biases of seven Fourier-based implementations. Our analyses show that truncation and discretization errors significantly increase as we move away from the Black-Scholes-Merton framework. We rank the…
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…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…