The `volatility smile' is one of the well-known biases of Black-Scholes models for pricing options. In this paper, we introduce a robust method of reducing this bias by pricing subject to a deterministic functional volatility = (S; t). This instantaneous volatility is chosen as a spline whose weights are determined by a regularised numerical strategy that approximately minimises the di erence b...

Following the framework of Çetin, Jarrow and Protter [4] we study the problem of super-replication in presence of liquidity costs under additional restrictions on the gamma of the hedging strategies in a generalized Black-Scholes economy. We find that the minimal super-replication price is different from the one suggested by the Black-Scholes formula and is the unique viscosity solution of the ...

Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black-Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches: nonlinear and quantum, both based on (adaptive form of) the Schrödinger equation. The nonlinear approach comes in two flavors: for the case of constant volat...

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

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 ...

This paper deals with the numerical solution of Black–Scholes option pricing partial differential equations by means of semidiscretization technique. For the linear case a fourth-order discretization with respect to the underlying asset variable allows a highly accurate approximation of the solution. For the nonlinear case of interest modeling option pricing with transaction costs, semidiscreti...

Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...

We compare two methods for superreplication of options with convex pay-off functions. One method entails an overestimation of the unknown covariance matrix in the sense of quadratic forms. With this method the value of the superreplicating portfolio is given as the solution of a linear Black-Scholes type equation. In the second method the choice of quadratic form is made pointwise. This leads t...

The maximality principle [6] is shown to be valid in some examples of discounted optimal stopping problems for the maximum process. In each of these examples explicit formulas for the value functions are derived and the optimal stopping times are displayed. In particular, in the framework of the Black-Scholes model, the fair prices of two lookback options with infinite horizon are calculated. T...