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.
Original language | English |
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Pages (from-to) | 99-110 |
Number of pages | 12 |
Journal | Journal of Econometrics |
Volume | 196 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2017 |
Bibliographical note
Publisher Copyright:© 2016 Elsevier B.V.
Funding
Second author’s support is acknowledged from the NSF under Grant No. SES 1258258 and Grant NRF-2014S1A2A2027803 from the Korean Government . First author’s support from Israel Science Foundation Grant No. 1082-14 and from the Sapir Center in Tel Aviv University is gratefully acknowledged.
Funders | Funder number |
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National Science Foundation | SES 1258258, NRF-2014S1A2A2027803 |
Directorate for Social, Behavioral and Economic Sciences | 1258258 |
Israel Science Foundation | 1082-14 |
Center for Nanoscience and Nanotechnology, Tel Aviv University |
Keywords
- Autoregression
- Derivative
- Diffusion
- Options
- Similarity
- Stochastic unit root
- Time-varying coefficients