Related papers: Pricing American options via multi-level approxima…
The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal non-asymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some…
Consider a discrete finite-dimensional, Markovian market model. In this setting, discretely sampled American options can be priced using the so-called ``non-recombining'' tree algorithm. By successively increasing the number of exercise…
Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair…
In this paper we propose a new method of estimation for discrete choice demand models when individual level data are available. The method employs a two-step procedure. Step 1 predicts the choice probabilities as functions of the observed…
We consider the pricing of VIX options in the rough Bergomi model. In this setting, the VIX random variable is defined by the one-dimensional integral of the exponential of a Gaussian process with correlated increments, hence approximate…
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…
In this paper, we present a reduced basis method for pricing European and American options based on the Black-Scholes and Heston model. To tackle each model numerically, we formulate the problem in terms of a time dependent variational…
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…
This paper is devoted to pricing American options using Monte Carlo and the Malliavin calculus. Unlike the majority of articles related to this topic, in this work we will not use localization fonctions to reduce the variance. Our method is…
Characterization of the American put option price is still an open issue. From the beginning of the nineties there exists a non-closed formula for this price but nontrivial numerical computations are required to solve it. Strong efforts…
In this work, we develop a novel efficient quadrature and sparse grid based polynomial interpolation method to price American options with multiple underlying assets. The approach is based on first formulating the pricing of American…
Fast pricing of American-style options has been a difficult problem since it was first introduced to financial markets in 1970s, especially when the underlying stocks' prices follow some jump-diffusion processes. In this paper, we propose a…
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift,…
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…
We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…
We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average…
The pricing and hedging of a general class of options (including American, Bermudan and European options) on multiple assets are studied in the context of currency markets where trading is subject to proportional transaction costs, and…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
We present a novel method for the numerical pricing of American options based on Monte Carlo simulation and the optimization of exercise strategies. Previous solutions to this problem either explicitly or implicitly determine so-called…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…