Olkhov, Victor (2020): Classical Option Pricing and Some Steps Further.
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Abstract
This paper takes the trade dataset of the value C and the volume V of executed transactions and regards relations C=pV as the only definition of the implemented price p. Any other price definitions, price models and forecasts form agents price expectations. Expectations force agents perform transactions and thus impact the price p dynamics. This paper considers the classical BlackScholesMerton (BSM) model for the underline asset price determined by the trade dataset and takes into account agents expectations. We show that the BSM model implicitly uses assumption that the value and the volume of transactions follow identical Brownian processes. Violation of this identity leads to 2dimensional BSMlike equation with two constant volatilities. The impact of agents expectations can further increase the dimension of the BSM model. Agents expectations may depend on the option price data and that can lead to 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:  103601 
Depositing User:  Victor Olkhov 
Date Deposited:  22 Oct 2020 06:45 
Last Modified:  22 Oct 2020 06:45 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/103601 
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