Seyed-Mohammad-Mahdi Kazemi

Seyed-Mohammad-Mahdi Kazemi
Kharazmi University | KHU · Department of Finance

Assistant Professor at Kharazmi University Department of Finance

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2
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21
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Publications

Publications (2)
Article
Full-text available
In this paper, we introduce a new family of infinitely smooth and “nearly” locally supported radial basis functions (RBFs), derived from the general solution of a heat equation arising from the American option pricing problem. These basis functions are expressed in terms of “the repeated integrals of the complementary error function” and provide hi...
Article
Full-text available
Our aim in this paper is to approximate the price of an American call option written on a dividend-paying stock close to expiry using an asymptotic analytic approach. We use the heat equation equivalent of the Black–Scholes partial differential equation defined on an unbounded spatial domain and decompose it into inner and outer problems. We extend...

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Projects

Projects (2)
Project
In this paper, we will propose a new approach to approximate the price of an American call option written on a dividend-paying risky underlying following a jump-diffusion process. Taking into account the fact that the pricing partial integro-differential equation (PIDE) in this case is defined in an unknown and unbounded domain, we will employ the well-developed artificial boundary approach to reduce the infinite "physical" domain into a finite "computational" one and to gain considerable efficiency in this respect. Using the Fourier transform approach, we introduce an exact non-local boundary condition on this artificial (transparent) boundary. We prove some properties of the optimal early exercise boundary of the option in this case which helps us to locate the place of the free boundary during the course of the solution procedure. We then develop a Crank-Nicolson scheme to solve the PIDE along with the artificial boundary condition. Our results show that the proposed approach is efficient and gives a better accuracy than other alternatives from the literature.
Archived project
In this paper, we introduce a new family of infinitely smooth and “nearly” locally supported radial basis functions (RBFs), derived from the general solution of a heat equation arising from the American option pricing problem. These basis functions are expressed in terms of “the repeated integrals of the complementary error function” and provide highly efficient tools to solve the free boundary partial differential equation resulting from the related option pricing model. We introduce an integral operator with a function-dependent lower limit which is employed as a basic tool to prove the radial positive definiteness of the proposed basis functions and could be of independent interest in the RBF theory. We then show that using the introduced functions as expansion bases in the context of an RBF-based meshless collocation scheme, we could exactly impose the transparent boundary condition accompanying the heat equation. We prove that the condition numbers of the resulting collocation matrices are orders of magnitude less than those arising from other popular RBF families used in current literature. Some other properties of these bases such as their Fourier transforms as well as some useful representations in terms of positive Borel measures will also be discussed.