Classical Option Pricing and Some Steps Further

Victor Olkhov

MPRA Paper from University Library of Munich, Germany

Abstract: This paper modifies single assumption in the base of classical option pricing model and derives further extensions for the Black-Scholes-Merton equation. We regard the price as the ratio of the cost and the volume of market transaction and apply classical assumptions on stochastic Brownian motion not to the price but to the cost and the volume. This simple replacement leads to 2-dimensional BSM-like equation with two constant volatilities. We argue that decisions on the cost and the volume of market transactions are made under agents expectations. Random perturbations of expectations impact the market transactions and through them induce stochastic behavior of the underlying price. We derive BSM-like equation driven by Brownian motion of agents expectations. Agents expectations can be based on option trading data. We show how such expectations can lead to nonlinear BSM-like equations. Further we show that the Heston stochastic volatility option pricing model can be applied to our approximations and as example derive 3-dimensional BSM-like equation that describes option pricing with stochastic cost volatility and constant volume volatility. Diversity of BSM-like equations with 2 – 5 or more dimensions emphasizes complexity of option pricing problem. Such variety states the problem of reasonable balance between the accuracy of asset and option price description and the complexity of the equations under consideration. We hope that some of BSM-like equations derived in this paper may be useful for further development of assets and option market modeling.

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
New Economics Papers: this item is included in nep-cfn, nep-fmk and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/99918/1/MPRA_paper_99918.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/103601/1/MPRA_paper_99918.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:99918

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 ().