We examine a Markov tree (MT) model for option pricing in which the dynamics of the underlying asset are modeled by a non-IID process. We show that the discrete probability mass function of log returns generated by the tree is closely approximated by a continuous mixture of two normal...

Lewis and Mordecki have computed the Wiener–Hopf factorization of a Lévy process whose restriction of the Lévy measure on ]0,+∞[ has a rational Laplace transform. This allowed them to compute the distribution of (Xt,inf0≤s≤tXs). For the same class of Lévy processes, we compute the...

In this paper, we propose a new type of derivative called a pattern derivative. In the simple case of an asset that moves up u or down d in value, a pattern is a sequence of {u, d} movements that may occur before expiration. We provide general pricing formulas that rely on a brute force approach...

We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing, for example, in a multivariate analysis of financial time series, and displaying both inter-asset cross-covariances and temporal auto-covariances. We give a comprehensive...

In 1973, Fisher Black, Myron Scholes and separately Robert Merton derived the Black-Scholes-Merton (BSM) model, which was rewarded the Nobel Prize in 1997. Despite its limitations, the model has survived until today as the dominant pricing model for standard and exotic European style options....

Requiring companies to expense options in the absence of any satisfactory method to evaluate their costs would be inconsistent with the principles and objectives of accounting.

Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationship between the shape of the market impact function describing the average response of the market...

Models with two or more risk sources have been widely applied in option pricing in order to capture volatility smiles and skews. However, the computational cost of implementing these models can be large—especially for American-style options. This paper illustrates how numerical techniques...