Publication Type

Journal Article

Publication Date

1-2017

Abstract

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.

Keywords

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

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

196

Issue

1

First Page

99

Last Page

110

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2016.05.019

Publisher

Elsevier

Copyright Owner and License

Authors

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://doi.org/10.1016/j.jeconom.2016.05.019

Included in

Econometrics Commons

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