The Interesting Complexity of Option Pricing: An Introduction to Black-Scholes Theory
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Posted On :
Mar-04-2010
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Article Word Count :
432
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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.
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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 that thing when you dont even have a beginners guide is exactly like driving to a new city or location without even having a simple map with you. No doubt it is difficult to explain 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. It is essential for us to understand that, yes, users may be able to consider all assets and cash flows to be risk free, but when it comes to investing, no investor can actually be risk-free or even risk neutral. Risk neutral theory as you can see is not a reflection of the occurrences in 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.
Ross and Cox formulated this technique. After three years of validation, they realized the actual application and, of course, importance of the method. The details and mathematical structure of the risk neutral method was formalized by Ross and Cox once they decided to publish the papers 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. Exploring numerical solutions is the primary usage, here the user is lead towards closed form solutions. The Black Scholes model changed the often puzzling game of guessing of the world market into science by decoding the risk management and finance. A large number of financial derivatives and stock options had been using this model a lot to expand themselves. Once Robert Merton amended and rectified the formula, this black scholes model is extensively used by other market segments like mortgages and student loans.
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Article Source :
http://www.articleseen.com/Article_The Interesting Complexity of Option Pricing: An Introduction to Black-Scholes Theory_12448.aspx
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Author Resource :
Author writes on various topics of interest like option pricing black scholes
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Keywords :
option pricing black scholes,
Category :
Finance
:
Investing
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