We have written S = S(t); B = B(t); V = V (t) and dW = dW (t) for notational convenience. We also assume the portfolios are self-…nancing, which implies that changes in portfolio value are due to changes in the value of the three instruments, and nothing else. Under this setup, any of the instruments can be replicated by forming a replicating portfolio of the other two instruments, using the co...

We consider statistical ensembles of Schwarzschild black holes and prove that these ensembles describe black holes of non vanishing temperatures. The mean space-times associated to these ensembles are explored through exact computations of their energy distributions, total masses and calorific capacities. We discuss our results, with special emphasis on their connections with current and near f...

The multi-parameter character of supersymmetric dark-matter models implies the combination of their experimental studies with astrophysical and cosmological probes. The physics of the early Universe provides nontrivial effects of non-equilibrium particles and primordial cosmological structures. Primordial black holes (PBHs) are a profound signature of such structures that may arise as a cosmolo...

A. Belhaj, M. Chabab,b,1 H. El Moumni, K. Masmar, M.B. Sedra and A. Segui Département de Physique, Faculté Polydisciplinaire, Université Sultan M. Slimane, Béni Mellal, Morocco High Energy Physics and Astrophysics Laboratory, FSSM, Cadi Ayyad University, Marrakesh, Morocco Université Mohammed Premier, Ecole Nationale des Sciences Appliquées, Al Hoceima, Morocco Département de Physique, LHESIR, ...

One of the developments in options market is formation various pricing models for an option to help buyer determine fairness price. Black-Scholes model uses assumption that log return price stocks normally distributed, while reality, real-world couldn’t fit into assumption. To be able obtain calculation considers skewness and kurtosis stock data, there are many alternative methods, namely with ...

This paper uses risk-adjusted lognormal probabilities to derive the BlackScholes formula and explain the factors N(d1) and N(d2). It also shows how the one-period and multi-period binomial option pricing formulas can be restated so that they involve analogues of N(d1) and N(d2) which have the same interpretation as in the Black-Scholes model. Cet article utilise les probabilités lognormaux corr...

A better understanding of the empirical dynamics of Black-Scholes implied volatility surface has long been of considerable interest to both practitioners and academics. Basing on some findings about the ad hoc Black-Scholes valuation approach suggested in Dumas, Flemming and Whaley (1998), this essay studies the empirical performance of various volatility function forms that characterize the re...

Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, 2, 415-431, 2002) to include volatility-stock correlations consistent with the leverage effect. A generalized Black-Scholes partial differential equation for this model is obtained, together ...