The developers of the Black Scholes Model, Fischer Black, Myron Scholes and Robert
Merton designed this mathematical formula to assign prices to European options.
It was designed in 1973 to create a valuation model for stock warrants.
Background history of the celebrated founders:
Myron
Scholes completed his Ph.D. in 1968 and joined the MIT Sloan School of
Management in the field of academics where he met Fischer Black who was an
independent consultant and had obtained a PhD in applied mathematics from
Harvard University. They both later met Robert Merton who
joined MIT in 1970. The years that followed the three geniuses did
groundbreaking research on a model for pricing stock options and came up with
their own mathematical formula known today as the Black Scholes Merton formula.
In 1981 Scholes went to Stanford University where he held the position of a
teacher till his retirement in 1996. In the year 1997 the he and Robert Merton
were awarded a shared Nobel Prize for Economics. The Nobel Prize Committee paid
special tribute to their co founder Fischer Black and said that he too would
have shared in the glory had he not had passed away at that time. Meanwhile
Robert Merton completed his doctorate in economics and moved on to the MIT
Sloan School of Management where he taught till 1988. After then he moved to
Harvard University and retired in 1998. After that he rejoined MIT Sloan School
of Management.
For a layman the greatly engineered formula
may be difficult to grasp as it involves many complex mathematical rules. However
to comprehend its purpose and consequences, it is important to look at the
formula in simplified version.
What is meant by Option?
In simple
terms European call option is to employ your right to enter into a contract to
buy an asset but not being held obligatory to buy it at a certain given time
only. The asset will have to be bought at a predetermined price and at a
predetermined time but the authority to choose the right time and right price
to buy that asset remains with the buyer of the asset.
But to enter
into the contract, the buyer has to pay an upfront amount which is called the
Premium. The premium for each asset will be different and will be dependent on
its performance in the stock market.
Expected value of an option:
To calculate
the right value of your option contract you would have to check its volatility.
Volatility is simply the amount of times a stock moves over. If a certain stock
moves abundantly then it is said to have a higher volatility and therefore its
options will be tagged with a higher value in the market.
Understanding strike price:
The strike
price can be defined as the price at which the option contract can be
implemented. It is very important to understand strike price as it is the basic
element of the Black Scholes Model. At the date of expiration the difference
calculated on the market price of the stock and the option’s strike price is
the profit earned on implementing the option.
The Black
Scholes Model uses these five basic inputs to determine the price of the
financial tools:
These inputs are:
·
Underlying
price
·
Strike
price
·
Days
left till the expiry date
·
Dividends
·
Current
volatility
The Black Scholes Model
The model is
used to determine the value of options. It theorizes that the option price
follows a Brownian motion with continuous drift and volatility. When used on a
stock option the model inserts the price variation of the stock which is
constant, the value of money in relation to time, the strike price of the
option and the time left till option’s expiry.
The Black Scholes Model does not
require the understanding of calculus for correct interpretation and accurate
results. However, the knowledge of the above explained terms in mandatory to
understand the concept behind the Black Scholes Model.
The advantages of the Black Scholes
formula:
It is known
as one of the most accurate financial formula in the market as it calculates
the price of the option quite accurately. The calculation usually matches the
actual price very closely. Moreover it provides investors an insight to options
price and its relation to stock price movements. This in turn maximizes the
security platform for the investors as they can implement portfolio insurance
more effectively.
The model is
a great way to keep the market consistently peaceful as it can accurately sum up
the equilibrium pricing relationships.
Some of the disadvantages of Black
Scholes formula:
It sometimes
misquotes options that are paying a high dividend stock. Furthermore, it also
takes into account the under rated fact that the risk free rate and the stock’s
volatility are constant. Moreover, it states that the prices of stock are
steady and are not subjected to major changes such as a merger, or a takeover. Lastly
the model signifies that no dividends are received on stocks until the date of
expiration. These are some of the limitations of the Black Scholes formula
which dampen its uniqueness and accuracy.
