A multivariate stochastic unit root model with an application to derivative pricing

Offer Lieberman, Peter C.B. Phillips

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23 Scopus citations


This paper extends recent findings of Lieberman and Phillips (2014) on stochastic unit root (STUR) models to a multivariate case including asymptotic theory for estimation of the model's parameters. The extensions are useful for applications of STUR modeling and 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 substantially reduces the average percentage pricing error of the Black–Scholes and Heston's (1993) stochastic volatility (with zero volatility risk premium) pricing schemes in most moneyness-maturity categories considered.

Original languageEnglish
Pages (from-to)99-110
Number of pages12
JournalJournal of Econometrics
Issue number1
StatePublished - 1 Jan 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.


  • Autoregression
  • Derivative
  • Diffusion
  • Options
  • Similarity
  • Stochastic unit root
  • Time-varying coefficients


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