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Classical Option Pricing and Some Steps Further

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  • Olkhov, Victor

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.

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  • Olkhov, Victor, 2020. "Classical Option Pricing and Some Steps Further," MPRA Paper 105431, University Library of Munich, Germany, revised 28 Dec 2020.
    • Handle: RePEc:pra:mprapa:105431
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    Cited by:

    1. Victor Olkhov, 2022. "Market-Based Asset Price Probability," Papers 2205.07256, arXiv.org, revised Feb 2024.
    2. Olkhov, Victor, 2022. "Why Economic Theories and Policies Fail? Unnoticed Variables and Overlooked Economics," MPRA Paper 114187, University Library of Munich, Germany.
    3. Olkhov, Victor, 2022. "Introduction of the Market-Based Price Autocorrelation," MPRA Paper 112003, University Library of Munich, Germany.
    4. Olkhov, Victor, 2022. "Economic Policy - the Forth Dimension of the Economic Theory," MPRA Paper 112685, University Library of Munich, Germany.
    5. Olkhov, Victor, 2022. "Price and Payoff Autocorrelations in the Consumption-Based Asset Pricing Model," MPRA Paper 112255, University Library of Munich, Germany.
    6. Olkhov, Victor, 2021. "To VaR, or Not to VaR, That is the Question," MPRA Paper 105458, University Library of Munich, Germany.

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    More about this item

    Keywords

    Option Pricing; Black-Scholes-Merton Equations; Stochastic Volatility; Market Transactions; Expectations; Nonlinear equations;
    All these keywords.

    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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