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Using Multivariate Densities to Assign Lattice Probabilities When There Are Jumps

Jimmy E. Hilliard and Jitka Hilliard

Journal of Futures Markets, 2015, vol. 35, issue 4, 385-398

Abstract: The lattice approximation to a continuous time process is an especially useful way to value American and real options. We choose lattice probabilities by extending density matching for diffusions to density matching for jump diffusions. Technically, this requires that diffusion and jump components be cast as independent state variables. In this setup, the diffusion probabilities are locally normal and the jump probabilities are locally a mixture of distributions. The lattice is structurally uniform and density matching ensures that all probabilities are legitimate without requiring jumps to non‐adjacent nodes. The approach generalizes easily to several state variables, does not require node adjustments, and does not appear to be dominated by more specialized numerical algorithms. We demonstrate the model for scenarios where the option may depend on a jump diffusion with possible stochastic interest rates and convenience yields. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:385–398, 2015

Date: 2015
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