Olkhov, Victor (2020): Classical Option Pricing and Some Steps Further.
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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 of this definition 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 2dimensional BSMlike equation with two constant volatilities. We show that agents expectations those approve execution of transactions can further 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 BSMlike equations. We reconsider the Heston stochastic volatility model for the price determined by the value and the volume and derive 3dimensional BSMlike model with stochastic value volatility and constant volume volatility. Variety of the BSMlike equations states the problem of reasonable balance between the accuracy and the complexity of the option pricing equations.
Item Type:  MPRA Paper 

Original Title:  Classical Option Pricing and Some Steps Further 
English Title:  Classical Option Pricing and Some Steps Further 
Language:  English 
Keywords:  Option Pricing; BlackScholesMerton Equations; Stochastic Volatility; Market Transactions; Expectations; Nonlinear equations 
Subjects:  G  Financial Economics > G1  General Financial Markets G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates G  Financial Economics > G1  General Financial Markets > G17  Financial Forecasting and Simulation 
Item ID:  106243 
Depositing User:  Victor Olkhov 
Date Deposited:  25 Feb 2021 07:52 
Last Modified:  25 Feb 2021 07:52 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/106243 