Related papers: Efficient European and American option pricing und…
We apply path integration techniques to obtain option pricing with stochastic volatility using a generalized Black-Scholes equation known as the Merton and Garman equation. We numerically simulate the option prices using the technique of…
Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a…
We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a…
The paper summarizes key results of the benchmark approach with a focus on the concept of benchmark-neutral pricing. It applies these results to the pricing of an extreme-maturity European put option on a well-diversified stock index. The…
In mathematical finance a popular approach for pricing options under some Levy model is to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE)…
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate…
In this paper a simple, effective adaptation of Alternating Direction Implicit (ADI) time discretization schemes is proposed for the numerical pricing of American-style options under the Heston model via a partial differential…
Semi-analytical pricing of American options in a time-dependent Ornstein-Uhlenbeck model was presented in [Carr, Itkin, 2020]. It was shown that to obtain these prices one needs to solve (numerically) a nonlinear Volterra integral equation…
This work examines a stochastic volatility model with double-exponential jumps in the context of option pricing. The model has been considered in previous research articles, but no thorough analysis has been conducted to study its quality…
The paper investigates the performance of the European option price when the log asset price follows a rich class of Generalized Tempered Stable (GTS) distribution. The GTS distribution is an alternative to Normal distribution and…
In this paper, we are presenting a method for estimation of market parameters modeled by jump diffusion process. The method proposed is based on Gibbs sampler, while the market parameters are the drift, the volatility, the jump intensity…
This paper is a contribution to the Proceedings of the Workshop Complexity, Metastability and Nonextensivity held in Erice 20-26 July 2004, to be published by World Scientific. We propose a generalization to Merton's model for evaluating…
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…
The paper focuses on pricing European-style options on several underlying assets under the Black-Scholes model represented by a nonstationary partial differential equation. The proposed method combines the Galerkin method with…
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…
Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to…
We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process. The analysis for out-of-the-money Asian options…
We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex…
An analytic method for pricing American call options is provided; followed by an empirical method for pricing Asian call options. The methodology is the pricing theory presented in "A Modern Theory of Random Variation", by Patrick…
In this paper, we present a very fast Monte Carlo scheme for additive processes: the computational time is of the same order of magnitude of standard algorithms for Brownian motions. We analyze in detail numerical error sources and propose…