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A recursive pricing method for autocallables under multivariate subordination

Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada

In this paper we develop a new class of models for pricing autocallables based on multivariate subordinate Orstein Uhlenbeck (OU) processes. Starting from d independent OU processes and an independent d-dimensional Lévy subordinator, we construct a new process by time changing each of the OU processes with a coordinate of the Lévy subordinator. The prices of underlying assets are then modeled as an exponential function of the subordinate processes. The new models introduce state-dependent jumps in the asset prices and the dependence among jumps is governed by the Lévy measure of the d-dimensional subordinator. By employing the eigenfunction expansion technique, we are able to derive the analytical formulas for the worst-of autocallable prices. We also numerically implement a specific model and test its sensitivity to some of the key parameters of the model.
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Keywords autocallables; multivariate assets; eigenfunction expansion; multivariate subordination; stochastic time change; OU process; jump diffusion

Citation: Kevin Z. Tong. A recursive pricing method for autocallables under multivariate subordination. Quantitative Finance and Economics, 2019, 3(3): 440-455. doi: 10.3934/QFE.2019.3.440


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