Related papers: American Options with Discontinuous Two-Level Caps

We study the obstacle problem associated with the American chooser option. The obstacle is given by the maximum of an American call option and an American put option, which, in turn, can be expressed as the maximum of the solutions to the…

In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] for perpetual American options when the Call-Put payoff $(y-x)^+$ is replaced by $\phi(x,y)$. It turns out that the duality still holds under…

We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset…

Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to…

The aim of this study was to develop methods for evaluating the American-style option prices when the volatility of the underlying asset is described by a stochastic process. As part of this problem were developed techniques for modeling…

This paper starts by defining the criteria where the early-exercise of an American option is never optimal, under positive, or negative rates. It follows with a short analysis of the various shapes of the exercise region under negative…

We present the method of moments approach to pricing barrier-type options when the underlying is modelled by a general class of jump diffusions. By general principles the option prices are linked to certain infinite dimensional linear…

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…

This paper is concerned with the solution of the optimal stopping problem associated to the valuation of Perpetual American options driven by continuous time Markov chains. We introduce a new dynamic approach for the numerical pricing of…

We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal…

In practical work with American put options, it is important to be able to know when to exercise the option, and when not to do so. In computer simulation based on the standard theory of geometric Brownian motion for simulating stock price…

American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and…

In this paper we analyze American style of floating strike Asian call options belonging to the class of financial derivatives whose payoff diagram depends not only on the underlying asset price but also on the path average of underlying…

We call a given American option representable if there exists a European claim which dominates the American payoff at any time and such that the values of the two options coincide in the continuation region of the American option. This…

Using a fast numerical technique, we investigate a large database of investor suboptimal non-exercise of short maturity American call options on dividend-paying stocks listed on the Dow Jones. The correct modelling of the discrete dividend…

It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff…

The virtue of an American option is that it can be exercised at any time. This right is particularly valuable when there is model uncertainty. Yet almost all the extensive literature on American options assumes away model uncertainty. This…

We present three models of stock price with time-dependent interest rate, dividend yield, and volatility, respectively, that allow for explicit forms of the optimal exercise boundary of the finite maturity American put option. The optimal…

We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we…

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…