The construction of martingales with given marginal distributions at given times is a recurrent problem in financial mathematics. From a theoretical point of view, this problem is well-known as necessary and sufficient conditions for the existence of such martingales have been described....

We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson (1983). Our method allows for the close examination of the interpolation parameter on a rigorous theoretical footing instead of empirical...

Reformulating the results of del Baño Rollin, Ferreiro-Castilla, and Utzet (2010), we are able to give necessary and sufficient conditions for the moments of the stock price to exist and extend Theorem 2.1 of Forde and Jacquier (2011). Precisely Forde and Jacquier (2011) provide necessary...

This note identifies a gap in the proof of Corollary 2.4 in [2], which arises because the essential smoothness of the family (Xt/t) can fail for the log-spot process X in the Heston model, and describes how to circumvent the issue by applying a standard argument from large deviation theory

This paper presents a switching regime version of the Merton's structural model for the pricing of default risk. The default event depends on the total value of the firm's asset modeled by a Markov modulated Lévy process. The novelty of our approach is to consider that firm's asset jumps...

This paper reconsiders the predictions of the standard option pricing models in the context of incomplete markets. We relax the completeness assumption of the Black-Scholes (1973) model and as an immediate consequence we can no longer construct a replicating portfolio to price the option....

A numerical method to price options with moving barrier and time-dependent rebate is proposed. In particular, using the so-called Boundary Element Method, an integral representation of the barrier option price is derived in which one of the integrand function is not given explicitly but must be...

A numerical method to price double-barrier options with moving barriers is proposed. Using the so-called Boundary Element Method, an integral representation of the double-barrier option price is derived in which two of the integrand functions are not given explicitly but must be obtained solving...

Many efficient and accurate analytical methods for pricing American options now exist. However, while they can produce accurate option prices, they often do not give accurate critical stock prices. In this paper, we propose two new analytical approximations for American options based on the...