Z-Transform and preconditioning techniques for option pricing |
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Authors: | Gianluca Fusai Marina Marena Michael Ng |
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Affiliation: | 1. Department of Economic Science and Quantitative Methods (SEMeQ) , Università degli Studi del Piemonte Orientale , Novara , Italy;2. Department of Statistics and Applied Mathematics Diego de Castro , Università degli Studi di Torino , Torino , Italy;3. Department of Mathematics , Hong Kong Baptist University , Kowloon Tong , Hong Kong |
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Abstract: | In the present paper, we convert the usual n-step backward recursion that arises in option pricing into a set of independent integral equations by using a z-transform approach. In order to solve these equations, we consider different quadrature procedures that transform the integral equation into a linear system that we solve by iterative algorithms and we study the benefits of suitable preconditioning techniques. We show the relevance of our procedure in pricing options (such as plain vanilla, lookback, single and double barrier options) when the underlying evolves according to an exponential Lévy process. |
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Keywords: | Numerical methods for option pricing Exotic options Preconditioners Linear systems Toeplitz matrices |
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