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...

We study a discrete time hedging and pricing problem in a market with liquidity costs. Using Leland’s discrete time replication scheme [Leland, H.E., 1985. Journal of Finance, 1283–1301], we consider a discrete time version of the Black–Scholes model and a delta hedging strategy. We derive a partial differential equation for the option price in the presence of liquidity costs and develop a modi...

The multi-dimensional Black-Scholes equation is solved numerically for a European call basket option using a priori–a posteriori error estimates. The equation is discretized by a finite difference method on a Cartesian grid. The grid is adjusted dynamically in space and time to satisfy a bound on the global error at the expiry date. The discretization errors in each time step are estimated and ...

This paper deals with the Barles–Sonermodel arising in the hedging of portfolios for option pricing with transaction costs. This model is based on a correction volatility function Ψ solution of a nonlinear ordinary differential equation. In this paper we obtain relevant properties of the function Ψ which are crucial in the numerical analysis and computing of the underlying nonlinear Black–Schol...

This paper presents a numerical scheme that avoids iterations to solve the nonlinear partial differential equation system for pricing American puts with constant dividend yields. Upon applying a frontfixing technique to the Black-Scholes partial differential equation, a predictor-corrector finite difference scheme is proposed to numerically solve the discrete nonlinear scheme. In the comparison...

In this Paper, HomotopyPerturbation method (HPM) which is one of the most recent approximate analytical solutions is implemented to solve diffusion-convection-reaction equations (DCRE). The calculations are carried out for two different types of DCRE’s such as the Black-Scholes equation used in financial market option pricing and FokkerPlanck equation from plasma physics. The behavior of the ap...

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 ...

Market illiquidity, feedback e ects, presence of transaction costs, risk from unprotected portfolio Note 1: In the title, insert “a” or “the” before “Analytical”? and other nonlinear e ects in PDE-based option pricing models can be described by solutions to the generalized Black–Scholes parabolic equation with a di usion term nonlinearly depending on the option price itself. In this paper, di e...

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 ...