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...

We present an efficient and accurate finite-difference method for computing Black-Scholes partial differential equations with multiunderlying assets. We directly solve Black-Scholes equations without transformations of variables. We provide computational results showing the performance of the method for two underlying asset option pricing problems.

The analogue of Black–Scholes formula for vanilla call option price in conditions of (B, S)-securities market with delayed response is derived. A special case of continuous-time version of GARCH is considered. The results are compared with the results of Black and Scholes. © 2006 IMACS. Published by Elsevier B.V. All rights reserved.

‚robert merton, who’s best known for his academic work in developing option-pricing models, published his first scholarly paper on a topic far removed from finance: Gulliver’s Travels. While an undergraduate at Columbia University in New York, he wrote a piece for a literature class that analyzed the physical impossibility of a flying island as described in Jonathan Swift’s classic work. Merton...

Standard derivative pricing theory is based on the assumption of agents acting as price takers on the market for the underlying asset. We relax this hypothesis and study if and how a large agent whose trades move prices can replicate the payoff of a derivative security. Our analysis extends prior work of Jarrow to economies with continuous security trading. We characterize the solution to the h...