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The Evaluation of American Compound Option Prices Under Stochastic Volatility Using the Sparse Grid Approach

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Abstract

A compound option (the mother option) gives the holder the right, but not obligation to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we demonstrate a partial differential equation (PDE) approach to pricing American-type compound options where the underlying dynamics follow Heston’s stochastic volatility model. This price is formulated as the solution to a two-pass free boundary PDE problem. A modified sparse grid approach is implemented to solve the PDEs, which is shown to be accurate and efficient compared with the results from Monte Carlo simulation combined with the Method of Lines.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp245.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 245.

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Length: 19
Date of creation: 01 Feb 2009
Date of revision:
Handle: RePEc:uts:rpaper:245

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Keywords: American compound option; stochastic volatility; free boundary problem; sparse grid; combination technique; Monte Carlo simulation; method of lines;

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Cited by:
  1. Mahayni, Antje & Schoenmakers, John G.M., 2011. "Minimum return guarantees with fund switching rights—An optimal stopping problem," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1880-1897.

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