Related papers: Error bounds and convergence for American put opti…
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…
This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for…
In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed…
The value of an American option is the maximized value of the discounted cash flows from the option. At each time step, one needs to compare the immediate exercise value with the continuation value and decide to exercise as soon as the…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…
Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with…
This article presents fast lower and upper estimates for a large class of options: the class of constrained multiple exercise American options. Typical options in this class are swing options with volume and timing constraints, and passport…
We derive a recursive formula for arithmetic Asian option prices with finite observation times in semimartingale models. The method is based on the relationship between the risk-neutral expectation of the quadratic variation of the return…
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different…
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…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
The theme in this paper is the recombining binomial tree to price American put option when the underlying stock follows constant elasticity of variance(CEV) process. Recombining nodes of binomial tree are decided from finite difference…
In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given…
The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to…
This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown epoch beyond a predefined level. We consider the market in which an asset price is described by geometric L\'evy…
We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to the trading of the underlying asset. The algorithm computes the prices on recombining binomial trees,…
We introduce an algorithm for the pricing of finite expiry American options driven by L\'evy processes. The idea is to tweak Carr's `Canadisation' method, cf. Carr [9] (see also Bouchard et al [5]), in such a way that the adjusted algorithm…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American…
American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomised) stopping time. The introduction of…
We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction…