# Perpetual american call option pricing

Since mesh steps need to satisfy conditions 14 and 15we choose the number of mesh steps in the direction where is the number of mesh steps in the direction. We discretize the differential operator using the central difference scheme on the previous uniform mesh. In this paper, we present an perpetual american call option pricing finite difference scheme for pricing two-asset American options. The mesh point values of the finite difference approximation are denoted by. We measure the accuracy in the discrete maximum norm and the convergence rate.

The classical finite difference methods lead to some off-diagonal elements perpetual american call option pricing the coefficient matrix of the discrete operator due to the dominating first-order derivatives and the mixed derivative. In the next section, we will prove that the system matrix corresponding to the discrete operator is an M-matrix. The artificial boundary conditions at and are chosen to be. We consider the following two-asset American put option pricing model [ 2425 ]:

Hence, it is not easy to construct a discretization with good properties and accuracy for problems with mixed derivatives. To receive news and publication updates for Journal of Function Spaces, enter your email address in the box below. Yousuf [ 23 ] developed an exponential time differencing scheme with a splitting technique for pricing American options under stochastic volatility. We consider the following two-asset American put perpetual american call option pricing pricing model [ 2425 ]:

In Section 3the discretization method is described. We consider the following two-asset American put option pricing model [ 2425 ]: Journal of Function Spaces.

The mesh steps to the direction, direction, and direction are denoted by, and. The artificial boundary conditions at and are chosen to be. Journal of Function Spaces.

The artificial boundary conditions at and are chosen to be. The mesh point values of the finite difference approximation are denoted by. Journal of Function Spaces. These elements can lead to nonphysical oscillations in the perpetual american call option pricing solution [ 1718 ]. It is shown that the scheme is second-order convergent with respect to the spatial variables.

Subscribe to Table of Contents Alerts. American put option with parameters: Theory, Methods and Applicationsvol. Since mesh steps need to satisfy conditions 14 and 15we choose the number of mesh steps in the direction where is the number of mesh steps in the direction.

Under certain mesh step size limitations, we obtain a coefficient matrix with an M-matrix property, which ensures that the solutions are oscillation-free. If mesh steps satisfy conditions 14 and 15the difference scheme 13 satisfies the following error estimate: American put option with parameters:

Indexed in Science Citation Index Expanded. We develop an accurate finite difference scheme for pricing two-asset American put options. Together, they require that the following inequalities hold: Therefore, we use the double mesh principle to estimate the errors and compute the experiment convergence rates in our computed solution.