We study the convergence of at-the-money implied volatilities to the spot volatility in a general model with a Brownian component and a jump component of finite variation. This result is a consequence of the robustness of the Black–Scholes formula and of the central limit theorem for martingales.

This paper presents the contemporary Fundamental Theorem of Asset Pricing as being equivalent to approaches to pricing that emerged before 1700 in the context of Virtue Ethics. This is done by considering the history of science and mathematics in the thirteenth and seventeenth century. An explanation as to why these approaches to pricing were forgotten between 1700 and 2000 is given, along with...

This work provides an application of wavelet analysis to pricing and hedging path–dependent contingent claims within the framework of the Black–Scholes model.

The double barrier option is characterized by pay-off with strike K, maturity T, upper Su and lower Sd barrier levels and the corresponding rebates φu and φd which can be time dependent. We divide last four quantities by strike K and introduce new variables x = ln(S/K), xu = ln(Su/K), xd = ln(Sd/K). The value of European double barrier call option U(t, x) satisfies the extended Black-Scholes eq...

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, ...