Option replication with transaction cost under Knightian uncertainty

Zhongguo Lin, Liyan Han and Wei Li

Physica A: Statistical Mechanics and its Applications, 2021, vol. 567, issue C

Abstract: To price options using replication in imperfect markets, both Knightian uncertainty and transaction cost have to be taken into account. In this paper, we put an uncertainty factor into volatility, assume investors minimize the root mean square error of replication when they choose hedging ratio, and derive European option price by a recursive procedure. To avoid high transaction cost caused by continuous hedging, we establish a discrete and binomial replication model considering both uncertainty and transaction cost. Numerical examples imply that option price contains both risk premium and uncertainty premium, and it is an approximately linearly increasing function of transaction cost but a nonlinearly increasing function of uncertainty. Additionally, both uncertainty and transaction cost have effects on the price of the at-the-money option, but they almost have no impact on the price of deeply in-the-money or out-of-the-money options. Empirical analysis of the Shanghai 50ETF options market indicates that the Black–Scholes model tended to underestimate the market price, whereas our model better estimates market prices.

Keywords: Replication; Binomial tree; Uncertainty; Transaction cost; Non-Gaussian option pricing (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037843712030978X
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:567:y:2021:i:c:s037843712030978x

DOI: 10.1016/j.physa.2020.125680

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().