Perpetual Options on Multiple Underlyings

Peter W. Duck, Geoffrey W. Evatt and Paul V. Johnson

Applied Mathematical Finance, 2014, vol. 21, issue 2, 174-200

Abstract: We study three classes of perpetual option with multiple uncertainties and American-style exercise boundaries, using a partial differential equation-based approach. A combination of accurate numerical techniques and asymptotic analyses is implemented, with each approach informing and confirming the other. The first two examples we study are a put basket option and a call basket option, both involving two stochastic underlying assets, whilst the third is a (novel) class of real option linked to stochastic demand and costs (the details of the modelling for this are described in the paper). The Appendix addresses the issue of pricing American-style perpetual options involving (just) one stochastic underlying, but in which the volatility is also modelled stochastically, using the Heston (1993) framework.

Date: 2014
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DOI: 10.1080/1350486X.2013.825437

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