Assumptions of the Black-Scholes-Merton Option Valuation Model

Assumptions of the Black-Scholes-Merton Option Valuation Model

The Black-Scholes-Merton (BSM) model is an optional pricing model. Under this model, the underlying share prices evolve in continuous time and are characterized at any point in time by a continuous distribution rather than a discrete distribution.

The following key assumptions underpin the BSM model:

  1. The price of the underlying share follows a geometric Brownian motion. This implies that there are no jumps in share prices.
  2. There are no risk-free arbitrage opportunities.
  3. The risk-free rate of interest is constant, equal for all maturities, and identical for borrowing or lending.
  4. The volatility of the return of the underlying is known and constant.
  5. Unlimited short selling of the underlying is permitted.
  6. No taxes or transaction costs are payable.
  7. The underlying share can be traded continuously and in very small numbers of units.
  8. Early exercise of the options is not allowed (BSM, therefore, can only be used to value European options).

These assumptions result in a complete market.

Question

Which of the assumptions of the Black-Scholes-Merton Model is least accurate:

  1. There are no taxes or transaction costs.
  2. The risk-free rate of interest is known and constant. It is the same for all maturities, borrowing, and lending.
  3. Unlimited short selling is not allowed.

Solution

The correct answer is C.

Unlimited short selling is permitted. This means that we can sell securities that we do not own. This is a necessary assumption because to hedge a derivative whose price is positively correlated with that of the underlying asset – e.g., a call option, which will have a positive delta – we need to hold a negative quantity of the underlying asset.

A and B are assumptions of the BSM model. 

Reading 34: Valuation of Contingent Claims

LOS 34 (f) Identify assumptions of the Black–Scholes–Merton option valuation model.

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop Graduate Admission Exam Prep


    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.
    Nyka Smith
    Nyka Smith
    2021-02-18
    Every concept is very well explained by Nilay Arun. kudos to you man!
    Badr Moubile
    Badr Moubile
    2021-02-13
    Very helpfull!
    Agustin Olcese
    Agustin Olcese
    2021-01-27
    Excellent explantions, very clear!
    Jaak Jay
    Jaak Jay
    2021-01-14
    Awesome content, kudos to Prof.James Frojan
    sindhushree reddy
    sindhushree reddy
    2021-01-07
    Crisp and short ppt of Frm chapters and great explanation with examples.