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Review of Derivatives Research

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01-10-2016

Stochastic covariance and dimension reduction in the pricing of basket options

Authors: Marcos Escobar, Daniel Krause, Rudi Zagst

Published in: Review of Derivatives Research | Issue 3/2016

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Abstract

This paper presents a tailor-made method for dimension reduction aimed at approximating the price of basket options in the context of stochastic volatility and stochastic correlation. The methodology is built on a modification to the Principal Component Stochastic Volatility (PCSV) model, a stochastic covariance model that accounts for most stylized facts in prices. The method to reduce dimension is first derived theoretically. Afterwards the results are applied to a multivariate lognormal context as a special case of the PCSV model. Finally empirical results for the application of the method to the general PCSV model are illustrated.

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The eigenvalues can not be strictly zero otherwise some stocks would be redundant leading to arbitrage opportunities.

A different measure should be proposed if targeting the conditional distribution rather than the stationary, unconditional distribution.

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Title: Stochastic covariance and dimension reduction in the pricing of basket options
Authors: Marcos Escobar
Daniel Krause
Rudi Zagst
Publication date: 01-10-2016
Publisher: Springer US
Published in: Review of Derivatives Research / Issue 3/2016
Print ISSN: 1380-6645
Electronic ISSN: 1573-7144
DOI: https://doi.org/10.1007/s11147-016-9119-x