A Multivariate Stochastic Unit Root Model with an Application to Derivative Pricing

Offer Lieberman and Peter Phillips
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Offer Lieberman: Bar-Ilan University

No 1964, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper extends recent findings of Lieberman and Phillips (2014) on stochastic unit root (SUR) models to a multivariate case including a comprehensive asymptotic theory for estimation of the model's parameters. The extensions are useful because they lead to a generalization of the Black-Scholes formula for derivative pricing. In place of the standard assumption that the price process follows a geometric Brownian motion, we derive a new form of the Black-Scholes equation that allows for a multivariate time varying coefficient element in the price equation. The corresponding formula for the value of a European-type call option is obtained and shown to extend the existing option price formula in a manner that embodies the effect of a stochastic departure from a unit root. An empirical application reveals that the new model is consistent with excess skewness and kurtosis in the price distribution relative to a lognormal distribution.

Keywords: Autoregression; Derivative, Diffusion, Options, Similarity, Stochastic unit root, Time-varying coefficients (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 56 pages
Date: 2014-12
New Economics Papers: this item is included in nep-ecm and nep-ets
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Journal Article: A multivariate stochastic unit root model with an application to derivative pricing (2017)
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