Abstract In recent years a number of authors pointed out significant stability and convergence problems while using Cox-Ross-Rubinstein binomial method to price and hedge barrier options. Different modifications were suggested to improve the convergence and stability of the binomial method. However, as this article shows, lattice approach in general has limited stability factor when applied to ...

This paper questions one of the fundamental assumptions made in options pricing: that the daily returns of a stock are independent and identically distributed (IID). We apply an estimation procedure to years of daily return data for all stocks in the French CAC-40 index. We find six stocks whose log returns are best modeled by a first-orderMarkov chain, not an IID sequence. We further propose t...

In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As examples, the quantum model of binomial markets is studied. We show that this quantum model ceases to pose the paradox which appears in the classical model of...

A Corporation is a company that owns other companies outstanding stock. In business matters, a Corporation is a defaul company if, at least, one of its subsidiary is on default. The statistical interest is, in a specific period of time, to determine the Default probability for the Corporation given that the subsidiaries of this Corporation are correlated. Therefore, the model must address the i...

The present time, denoted at n = 0 and the expiration time, denoted at n = N . The lower case letter n, k (and occasionally i, j,m) will be used to denote the time variable. The notation Sk (or Sn, Si, Sj · · · ) denotes the value of the stock (the underlying) at time k (or time n, i, j · · · ). An important convention we’ll use is that S0 will always be a constant, that is the present value of...

Derivatives pricing and investment management seem to have little in common. Even at the organizational level, they belong to two quite separate parts of financial markets. The so-called sell side, represented mainly by the investment banks, among other things offers derivatives products to their customers. Some of them are wealth managers, belonging to the so-called buy side of financial marke...