The Interesting Complexity Of Option Pricing- An Introduction To Black-scholes Theory

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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. Yes, i mean 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. And just like in investing, we are facing the undeniably challenging
task of providing 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. While it may be tempting to use the option pricing theory
to any of your valuation, it is important that you understand that this method do not
provide or even attempted to give a realistic expected discount rates and even returns.
It is very important for us to understand that though you may consider all assets and
cash flow to be risk free, when it comes to investing, no investor can actually be
risk-free or even risk neutral. If you are hoping for the exact replica of the real world
happenings through the Risk neutral theory ,then this method must have by now
hinted to you that it will not. 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. It took numerous man hours and three years
of validation to realise the potential of this application and its importance. 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. Partial differential
equations approack is what is used in the Black Scholes theory, which use closed form
solutions guiding the user to get some simple pricing formulas.

Stochastic calculus is what is used by Black Scholes approach when one wants to
narrow down the difference between the risk neutral and real world statistics. While it
is primarily used to explore numerical solutions, Black Scholes is also used to lead the
user towards closed form solutions. BY decoding the risk management and finance,
the Black Scholes model changed the often puzzling game of guessing of the world
market into science. Stock options and other financial derivatives use this model
during their expansion period. Robert Merton is the pioneer who amended the black
scholes formula, making it possible for other financial market segment like students
loans and mortgages to use it.

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