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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…
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 study robust versions of pricing problems where customers choose products according to a generalized extreme value (GEV) choice model, and the choice parameters are not known exactly but lie in an uncertainty set. We show that, when the…
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…
In this paper, we introduce two novel methods to solve the American-style option pricing problem and its dual form at the same time using neural networks. Without applying nested Monte Carlo, the first method uses a series of neural…
We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can model volatility clustering and varying mean-reversion speeds of volatility. For pricing European options, we develop a…
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C…
Pricing of exotic financial derivatives, such as Asian and multi-asset American basket options, poses significant challenges for standard numerical methods such as binomial trees or Monte Carlo methods. While the former often scales…
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…
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…
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…
In this paper we propose an efficient method to compute the price of multi-asset American options, based on Machine Learning, Monte Carlo simulations and variance reduction technique. Specifically, the options we consider are written on a…
In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural…
Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…
The CEV model subsumes some of the previous option pricing models. An important parameter in the model is the parameter b, the elasticity of volatility. For b=0, b=-1/2, and b=-1 the CEV model reduces respectively to the BSM model, the…
In the present paper we present a finite element approach for option pricing in the framework of a well-known stochastic volatility model with jumps, the Bates model. In this model the asset log-returns are assumed to follow a…
We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)]. We develop new closed-form spectral expansions for pricing such options under a class…
We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation.…
A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual…
This paper studies equity basket options -- i.e., multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks -- and develops a new and innovative approach to ensure consistency between options…