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

• Main Authors: LIEBERMAN, Offer, Peter C. B. PHILLIPS
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2017
• Subjects: Autoregression; Derivative; Diffusion; Options; Similarity; Stochastic unit root; Time-varying coefficients; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1942; https://ink.library.smu.edu.sg/context/soe_research/article/2941/viewcontent/MultivariateStochasticUnitRootModel_2016_pp.pdf
• Institution: Singapore Management University

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.