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...

Black-Scholes equation as one of the most celebrated mathematical models has an explicit analytical solution known formula. Later variations equation, such fractional or nonlinear equations, do not have a closed form expression for corresponding In that case, will need asymptotic expansions, homotopy perturbation method, to give approximate solution. However, is non-smooth at special point. We ...

Since the 2007/2008 financial crisis, total value adjustment (XVA) should be included when pricing derivatives. In present paper, derivative values of European and American options have been priced where we take into account counterparty risk. Whereas considering risk already under Black-Scholes dynamics in [2], here novel contribution is introduction stochastic volatility resulting a Heston ty...

The celebrated Black-Scholes di.erential equation provides for the price of a 0nancial derivative. The uncertainty environment of such option price can be described by the classical ‘bit’: a system with two possible states. This paper argues for the introduction of a di.erent uncertainty environment characterized by the so called ‘qubit’. We obtain an information-based option price and discuss ...