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Stochastic Calculus and the Black-Scholes-Merton Model: A Simplified Approach

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  • Chang, Kuo-Ping

Abstract

In the continuous-time finance literature, it is claimed that the expected rate of return of underlying asset does not affect the option pricing model. This paper has shown that with no arbitrage, i.e., under the Arbitrage (Gordan) theorem, different underlying asset price processes used in the Black-Scholes-Merton partial differential equation and the Black-Scholes-Merton option pricing formula require that risk-free interest rate be a linear function of underlying asset’s expected rate of return (alpha) and variance of return, or (as in the literature) risk-free interest rate equal underlying asset's alpha.

Suggested Citation

  • Chang, Kuo-Ping, 2024. "Stochastic Calculus and the Black-Scholes-Merton Model: A Simplified Approach," MPRA Paper 122654, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:122654
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    File URL: https://mpra.ub.uni-muenchen.de/122654/1/MPRA_paper_122654.pdf
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    References listed on IDEAS

    as
    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    More about this item

    Keywords

    The Arbitrage (Gordan) theorem; Ito’s lemma; the Black-Scholes-Merton partial differential equation; the Black-Scholes-Merton option pricing formula.;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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