Related papers: Computing Greeks for L\'evy Models: The Fourier Tr…
We propose a new model for electricity pricing based on the price cap principle. The particularity of the model is that the asset price is an exponential functional of a jump L\'evy process. This model can capture both mean reversion and…
We prove and test an efficient series representation for the European Black-Scholes call, which generalizes and refines previously known approximations, and works in every market configuration.
Recent developments on financial markets have revealed the limits of Brownian motion pricing models when they are applied to actual markets. L\'evy processes, that admit jumps over time, have been found more useful for applications. Thus,…
In this note is presented a method, given nodal values on multidimensional nonconforming spectral elements, for calculating global Fourier-series coefficients. This method is ``exact'' in that given the approximation inherent in the…
Affine processes play an important role in mathematical finance and other applied areas due to their tractable structure. In the present article, we derive probabilistic representations and integration by parts (IBP) formulas for…
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent…
This work illustrates how several new pricing formulas for exotic options can be derived within a Levy framework by employing a unique pricing expression. Many existing pricing formulas of the traditional Gaussian model are obtained as a…
Motivated by a problematic coming from mathematical finance, this paper is devoted to existing and additional results of continuity and differentiability of the It\^o map associated to rough differential equations. These regularity results…
We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these…
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by L\'evy processes, extending earlier works…
In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed…
The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to…
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…
The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…
Financial markets based on L\'evy processes are typically incomplete and option prices depend on risk attitudes of individual agents. In this context, the notion of utility indifference price has gained popularity in the academic circles.…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
We present an adaptive approach for valuing the European call option on assets with stochastic volatility. The essential feature of the method is a reduction of uncertainty in latent volatility due to a Bayesian learning procedure. Starting…
In this paper, we derive the price of a European call option of an asset following a normal process assuming stochastic volatility. The volatility is assumed to follow the Cox Ingersoll Ross (CIR) process. We then use the fast Fourier…
The problem of European-style option pricing in time-changed L\'{e}vy models in the presence of compound Poisson jumps is considered. These jumps relate to sudden large drops in stock prices induced by political or economical hits. As the…
Despite significant advancements in machine learning for derivative pricing, the efficient and accurate valuation of American options remains a persistent challenge due to complex exercise boundaries, near-expiry behavior, and intricate…