This paper is devoted to the pricing of Barrier options by optimal quadratic quantization method. From a known useful representation of the premium of barrier options one deduces an algorithm similar to one used to estimate nonlinear filter using quadratic optimal functional quantization. Some numerical tests are fulfilled in the Black-Scholes model and in a local volatility model and a compari...

Double peak kHz QPO frequencies in neutron star sources varies in time by a factor of hundreds Hz while in microquasar sources the frequencies are fixed and located at the line ν2 = 1.5ν1 in the frequency-frequency plot. The crucial question in the theory of twin HFQPOs is whether or not those observed in neutron-star systems are essentially different from those observed in black holes. In blac...

We study the eeect of stochastic volatility on option prices. In the fast-mean reversion model for stochastic volatility of 5], we show that there is a full asymptotic expansion for the option price, centered at the Black-Scholes price. We show, however, that this price does not converge in a strong sense to Black-Scholes as the mean-reversion rate increases. We also introduce a general (possib...

We reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black–Scholes pricing formula, we propose a new method to obtain an explicit self–financing trading strategy expression for replications of claims in a general model. The main advantage of our method is that we propose using an orthogonal expansi...