This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game’s value to be continuous with respect to the time horizon are obtained using recent results on norm estimates for doubly reflected backward stochastic differenti...

Abstract The nonlinear differential equation option pricing formula is invaluable in financial derivatives investment risk assessment. This article applies the theory of equations to deal with risks commodity and currency markets. Through this condition, we obtain fair price process contingent rights under classic Black-Scholes model optimal growth strategy. results show that measurement stable...

In the complete model with stochastic volatility by Hobson and Rogers, preference independent options prices are solutions to degenerate partial differential equations obtained by including additional state variables describing the dependence on past prices of the underlying. In this paper, we aim to emphasize the mathematical tractability of the model by presenting analytical and numerical res...

We study the Black-Scholes model for American options with dividends. We cast the problem as a free-boundary problem for heat equations and use transformations to rewrite the problem in linear complementarity form. We use explicit and implicit finite difference methods to obtain numerical solutions. We implement and test the methods on a particular example in MATLABr. The effects of dividend pa...

in this paper, we try and valuate preemption rights by modifying the black-scholes model, which is widely used to valuate options and other derivatives. here we first present the basics of the black-scholes model and then we discus modification of the model to be fit for preemption right valuation. at the end, we valuate four of the preemptive rights using the proposed model

in this paper, the pricing of a european call option on the underlying asset is performed by using a monte carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. the proposed approach, applied in monte carlo simulation, is based on the black-scholes equation which generally def...

In this paper two different methods are presented to approximate the solution of the fractional Black-Scholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...