The Interesting Complexity of Option Pricing: An Introduction to Black-Scholes Theory

Most people, who essentially include almost everyone, when beginning their journey towards something, whether it’s investing in a new company or buying stocks, would prefer to have some sort-of definitive guide before they actually jump into the unknown. Right, who wouldn’t? Doing something that is undeniably new to you without a complete or even beginner’s guide is like driving to the unknown areas without a map. It is quite a challenging task to provide an overview of the Black-Scholes theory, or the root of the option pricing theory.

Using the equally famous Monte Carlo method which determines future asset values, the Black-Scholes theory being considered a risk neutral method has opened doors to different valuation methods. Though it is tempting to use the option pricing theory for your valuations, it is important to understand that this method do not provide or even attempt to give a realistic expected discount rates and returns. When you plan to invest on something though it seems like the assets and cash flow is risk free, please remember no investor is risk free or even neutral. As you can see Risk neutral theory by any means cannot give you the accurate idea of the occurrences of the real world. Nevertheless, most analysts love to use risk neutral theory because they know that when they use it correctly and accurately, the outcome still actually lands within the correct option prices.

The technique was essentially formulated by Ross and Cox. After three years of validation, they realized the actual application and, of course, importance of the method. Ross and Cox formalized the details and mathematical structure of the risk neutral method once they agreed to publish the paper along with Mark Rubinstein. The Black Scholes, also known as the differential equations approach, essentially uses the partial differential equations, which have closed-form solutions that can guide the user to achieve simple pricing formulas.

If you want to reduce the gap between real world statistics and risk neutral then stochastic calculus is used by Black Scholes approach to do it. Its primary usage is to explore numerical solutions and also to lead the user at closed form solutions. Essentially destined to decode risk management and finance, the Black Scholes model turned the guessing, which is often puzzling, game of the world market into science. Stock options and other financial derivatives use this model during their expansion period. Student loans and mortgages are other financial market segments which have been extensively using this Black Scholes formula after it has been amended by Robert Merton.

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