Classical Option Pricing and Some Steps Further

Victor Olkhov

MPRA Paper from University Library of Munich, Germany

Abstract: This paper considers the asset price p as relations C=pV between the value C and the volume V of the executed transactions and studies the consequences for the option pricing equations. We show that the classical BSM model implicitly assumes that value C and volume V of transactions follow identical Brownian processes. Violation of this identity leads to 2-dimensional BSM-like equation with two constant volatilities. We show that agents expectations can increase the dimension of the BSM model. We study the case when agents expectations may depend on the option price data and show that such assumption can lead to the nonlinear BSM-like equations. We reconsider the Heston stochastic volatility model for the price determined by the value and the volume and derive 3-dimensional BSM-like model with stochastic value volatility and constant volume volatility. Variety of the BSM-like equations states the problem of reasonable balance between the accuracy and the complexity of the option pricing equations.

Keywords: Option Pricing; Black-Scholes-Merton Equations; Stochastic Volatility; Market Transactions; Expectations; Nonlinear equations (search for similar items in EconPapers)
JEL-codes: G1 G12 G17 (search for similar items in EconPapers)
Date: 2020-04-27, Revised 2020-12-28
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/105431/8/MPRA_paper_105431.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/105431/1/MPRA_paper_99918.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/106243/1/MPRA_paper_106243.pdf revised version (application/pdf)

Related works:
Working Paper: Classical Option Pricing and Some Steps Further (2021)
Working Paper: Classical Option Pricing and Some Steps Further (2020)
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:pra:mprapa:105431

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().