Option Pricing Incorporating Factor Dynamics in Complete Markets

Yuan Hu, Abootaleb Shirvani, W. Brent Lindquist, Frank J. Fabozzi and Svetlozar T. Rachev
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Yuan Hu: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA
Abootaleb Shirvani: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA
W. Brent Lindquist: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA
Frank J. Fabozzi: Finance Department, EDHEC Business School, 393/400 Promenade des Anglais-BP3116, CEDEX 3, 06202 Nice, France
Svetlozar T. Rachev: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA

JRFM, 2020, vol. 13, issue 12, 1-33

Abstract: Using the Donsker–Prokhorov invariance principle, we extend the Kim–Stoyanov–Rachev–Fabozzi option pricing model to allow for variably-spaced trading instances, an important consideration for short-sellers of options. Applying the Cherny–Shiryaev–Yor invariance principles, we formulate a new binomial path-dependent pricing model for discrete- and continuous-time complete markets where the stock price dynamics depends on the log-return dynamics of a market influencing factor. In the discrete case, we extend the results of this new approach to a financial market with informed traders employing a statistical arbitrage strategy involving trading of forward contracts. Our findings are illustrated with numerical examples employing US financial market data. Our work provides further support for the conclusion that any option pricing model must preserve valuable information on the instantaneous mean log-return, the probability of the stock’s upturn movement (per trading interval), and other market microstructure features.

Keywords: path-dependent binomial option pricing; Donsker–Prokhorov invariance principle; Cherny–Shiryaev–Yor invariance principle; informed traders; statistical arbitrage based on forward contracts (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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