A new successive over-relaxation method to compute the Black-Scholes implied volatility is introduced. Properties of the new method are fully analyzed, including global well-definedness, local convergence, as well as global convergence. Quadratic order of convergence is achieved by either a...

In the framework of Black-Scholes-Merton option pricing models, by employing exotic options instead of plain options or warrants, this paper presents an equivalent decomposition method for usual Callable Convertible Bonds (CCB). Furthermore, the analytic valuation formulae for CCB are worked out...

We give a complete and self-contained proof of the existence of a strong solution to the free boundary and optimal stopping problems for pricing American path dependent options. The framework is su±ciently general to include geometric Asian options with non-constant volatility and recent...

The market evolution since the end of 2007 has been characterized by an increase of systemic risk and a high number of defaults. Realized recovery rates have been very dispersed and different from standard assumptions, while 60%-100% super-senior tranches on standard indices have started to...

Many e±cient 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...

We present an Hilbert space formulation for a set of implied volatility models introduced in \cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price $T$ an $K$, to be arbitrage free. The arbitrage free...

This is an introductory work to analytical properties of the futures market platform’s main parameters. The underlying mechanism of this market structure is formulated into a mathematical dynamical model. Some mathematical properties of traders’ positions, their potential and realized...

We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore we...

We develop an approximation technique for pricing finite-maturity timer options under Heston-like stochastic volatility models. By approximating the distributions of the accumulated variance and the random variance budget exceeding time, we obtain analytic expressions for timer option prices...

The probability density function for survivals, that is for transitions without hitting the barrier, for a collection of particles driven by correlated Brownian motions is analyzed. The analysis is known to lead one to a study of the spectrum of the Laplacian on domains on the sphere in higher...