Pricing American Options: A Duality Approach

Pricing American Options: A Duality Approach

We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close....

A Parallel Quasi-Monte Carlo Approach to Pricing American Options

Pricing American Options using Simulation

American options are financial contracts that allow exercise at any time until expiration. While the pricing of standard American option contracts has been well researched, with a few exceptions no analytical solutions exist. Valuation of more involved American option contracts, which include multiple underlying assets or pathdependent payoff, is still to a high degree an uncharted area. Most n...

An irregular grid approach for pricing high-dimensional American options ?

We propose and test a new method for pricing American options in a high-dimensional setting. The method is centred around the approximation of the associated complementarity problem on an irregular grid. We approximate the partial differential operator on this grid by appealing to the SDE representation of the underlying process and computing the root of the transition probability matrix of an ...

General Duality for Perpetual American Options

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 φ(x, y). It turns out that the duality still holds under monotonicity and concavity assumptions on φ. The specific analytical form of the Call-Put payoff only makes calculations easier but is not crucial unlike in the d...