A recursive pricing method for autocallables under multivariate subordination

Kevin Z. Tong; Kevin Z. Tong

doi:10.3934/QFE.2019.3.440

Quantitative Finance and Economics

2019, Volume 3, Issue 3: 440-455. doi: 10.3934/QFE.2019.3.440

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Research article

A recursive pricing method for autocallables under multivariate subordination

Kevin Z. Tong ^,

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

Received: 25 April 2019 Accepted: 05 June 2019 Published: 01 July 2019
JEL Codes: C02, G13

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.
- 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[J]. Quantitative Finance and Economics, 2019, 3(3): 440-455. doi: 10.3934/QFE.2019.3.440

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Abstract

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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