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Classical Option Pricing and Some Steps Further

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  • Victor Olkhov

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 2-dimensional BSM-like 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 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.

Suggested Citation

  • Victor Olkhov, 2020. "Classical Option Pricing and Some Steps Further," Papers 2004.13708, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:2004.13708
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    Cited by:

    1. Olkhov, Victor, 2022. "Introduction of the Market-Based Price Autocorrelation," MPRA Paper 112003, University Library of Munich, Germany.
    2. Olkhov, Victor, 2022. "Economic Policy - the Forth Dimension of the Economic Theory," MPRA Paper 112685, University Library of Munich, Germany.
    3. Victor Olkhov, 2022. "Market-Based Asset Price Probability," Papers 2205.07256, arXiv.org, revised Jan 2026.
    4. Olkhov, Victor, 2022. "Price and Payoff Autocorrelations in the Consumption-Based Asset Pricing Model," MPRA Paper 112255, University Library of Munich, Germany.
    5. Victor Olkhov, 2021. "To VaR, or Not to VaR, That is the Question," Papers 2101.08559, arXiv.org, revised Apr 2024.
    6. Victor Olkhov, 2022. "Why Economic Theories and Policies Fail? Unnoticed Variables and Overlooked Economics," Papers 2208.07839, arXiv.org.

    More about this item

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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