Related papers: Error analysis in Fourier methods for option prici…
In this article, we employ physics-informed residual learning (PIRL) and propose a pricing method for European options under a regime-switching framework, where closed-form solutions are not available. We demonstrate that the proposed…
We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar L\'evy-type stochastic processes. We derive rigorous error bounds for the…
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative…
We consider the discretized Bachelier model where hedging is done on an equidistant set of times. Exponential utility indifference prices are studied for path-dependent European options and we compute their non-trivial scaling limit for a…
We present an approximation method based on the mixing formula (Hull & White 1987, Romano & Touzi 1997) for pricing European options in Barndorff-Nielsen and Shephard models. This approximation is based on a Taylor expansion of the option…
In this paper, an integral equation representation for the early exercise boundary of an American option contract is considered. Thus far, a number of different techniques have been proposed in the literature to obtain a variety of integral…
We propose an offline-online procedure for Fourier transform based option pricing. The method supports the acceleration of such essential tasks of mathematical finance as model calibration, real-time pricing, and, more generally, risk…
Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the…
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…
The paper Borovkova et al. [4] uses moment matching method to obtain closed form formulas for spread and basket call option prices under log normal models. In this note, we also use moment matching method to obtain semi-closed form formulas…
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…
In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes…
The purpose of this paper is to analyze solutions of a non-local nonlinear partial integro-differential equation (PIDE) in multidimensional spaces. Such class of PIDE often arises in financial modeling. We employ the theory of abstract…
The Fourier-cosine expansion (COS) method is used to price European options numerically in a very efficient way. To apply the COS method, one has to specify two parameters: a truncation range for the density of the log-returns and a number…
A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign currency option is proposed…
One method to compute the price of an arithmetic Asian option in a Levy driven model is based on the exponential functional of the underlying Levy process: If we know the distribution of the exponential functional, we can calculate the…
In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…
We consider the problem of pricing American Exchange options driven by a L\'evy process. We study the properties of American Exchange options, we represented it as the sum of the price of the corresponding European exchange option price and…
Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of…
We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully examine the relation between the option prices, related partial…