Asian Options, Jump-Diffusion Processes on a Lattice, and Vandermonde Matrices
Asian options are options whose value depends on the average asset price during its lifetime. They are useful because they are less subject to price manipulations. We consider Asian option pricing on a lattice where the underlying asset follows the Merton–Bates jump-diffusion model. We describe the construction of the lattice using the moment matching technique which results in an equation system described by a Vandermonde matrix. Using some properties of Vandermonde matrices we calculate the jump probabilities of the resulting system. Some conditions on the possible jump sizes in the lattice are also given.
KeywordsAsset Price Option Price Underlying Asset Asian Option Vandermonde Matrix
This work was partially supported by The Royal Physiographic Society in Lund, The Swedish Foundation for International Cooperation in Research and Higher Education (STINT), The Swedish Research Council, The Royal Swedish Academy of Sciences, The Crafoord Foundation, as well as by The International Science Program, SIDA foundation and by Mälardalen University. Carolyne Ogutu is grateful to the research environment in Mathematics and Applied Mathematics at the Division of Applied Mathematics of the School of Education, Culture and Communication (UKK) at Mälardalen University for their hospitality and creating excellent conditions for research, research education and cooperation. She is also grateful for the support of the International Science Program, Uppsala University, Sweden, through collaboration with The Eastern African Universities Mathematics Programme. The authors would also like to thank the organisers of ICSIM and the referee whose report greatly improved the quality of the chapter.
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